Merged work sitting in bitbucket into local repo
will king
3 years ago
commit
7ec2ede00e
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Beamer Presentation
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% Version 1.0 (10/11/12)
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% This template has been downloaded from:
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% http://www.LaTeXTemplates.com
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% License:
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% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
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%
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% Changed theme to WSU by William King
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%----------------------------------------------------------------------------------------
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% PACKAGES AND THEMES
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%----------------------------------------------------------------------------------------
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%Import Preamble bits
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\input{../Assets/preambles/GeneralPreamble.tex}
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%----------------------------------------------------------------------------------------
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% TITLE PAGE
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%----------------------------------------------------------------------------------------
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\title[MDP Constellations]{Modeling decisions in operating satellite constellations}
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\author{Will King} % Your name
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\institute[WSU] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space
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{
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Washington State University \\ % Your institution for the title page
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\medskip
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\textit{william.f.king@wsu.edu} % Your email address
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}
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\date{\today} % Date, can be changed to a custom date
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\begin{document}
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\begin{frame}
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\titlepage % Print the title page as the first slide
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\end{frame}
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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Background}
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% Why should we care?
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% Uses of space
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% Pollution in space and it's impacts
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% Kessler Syndrome
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% What is different now
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%
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%
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%
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%-------------------------------------------------------------------------------------
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\begin{frame}
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\frametitle{Orbital Debris}
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%Story from monday ISS
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\href{https://edition.cnn.com/2021/11/15/politics/russia-anti-satellite-weapon-test-scn/index.html}{ISS threatened by debris cloud - Monday Nov 15th, 2021}
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\begin{itemize}
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\item Russia conducts an Anti-Satellite Missle Test generating at least 1,500 items of trackable debris
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\item The Astronauts and Cosmonauts on the ISS entered lockdown, including donning pressure suits.
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\item The situation is still being monitored although the immediate danger appears to have passed.
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\end{itemize}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Orbital Debris}
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Other events involving the ISS highlight the dangers from orbital debris:
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\begin{itemize}
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\item ISS conducts 3 evasive maneuvers to doge debris in 2020-
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\href{https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809}{Jerusalem Post}
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\item ISS hit by debris, May 2021- \href{https://www.asc-csa.gc.ca/eng/iss/news.asp}{Canadian Space Agency}
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\item ISS dodged debris from 2007 Anti-Sat Missile, Nov 2021-
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\href{https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809}{Jerusalem Post (Same as above)}
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\end{itemize}
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%This isn't a unique experience
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%list of other issues the ISS has faced
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Orbital Debris}
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%Talk about Fregat breakup
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Not just an issue for manned space flight.
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\href{https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv25i1.pdf}{Orbital Debris Quarterly News - NASA}
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\begin{itemize}
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\item In May of 2020, the Satellite SL-23 Zenit Fregat's
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tank suffered a second breakup event.
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\item While only 65 large pieces of debris were initially identified, by Feb. 2021
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over 325 had been attributed to the breakup.
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\item Debris was spread in orbits between 500km and 6,000km.
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\end{itemize}
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\href{https://www.yahoo.com/news/space-debris-russian-missile-test-175253044.html}{Starlink and recent Anti-Sat test}
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\begin{itemize}
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\item Estimated that there will likely be some impact to Starlink operations.
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\item 1,500 large pieces of debris initially identified.
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\end{itemize}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Why now?}
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%launch costs
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%nano-satellites
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In recent years two major changes have occured
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\begin{enumerate}
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\item New launch providers: SpaceX, RocketLab, etc have lead to plummeting launch costs
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\item CubeSates and other Nano-Satellites.
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\end{enumerate}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Goals}
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%Model decision making of satellite operators to be able to investigate policies to reduce kessler syndrome.
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Goals:
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\begin{itemize}
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\item Model the choices
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facing Satellite Constellation Operators
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and optimal policy policy response.
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\item Investigate the effect of various policies on debris pollution
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\end{itemize}
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\end{frame}
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%-------------------------------
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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
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\section{TOC}
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%-------------------------------------------------------------------------------------
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\begin{frame}[allowframebreaks] %Allow frame breaks
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\frametitle{Overview} % Table of contents slide, comment this out to remove it
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\tableofcontents
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%Planned TOC
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% See ../outline2.txt
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\end{frame}
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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Literature}
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%-------------------------------------------------------------------------------------
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\begin{frame}
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\frametitle{Past Literature}
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Key elements of recent literature.
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\begin{enumerate}
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\item \cite{Kessler1978}: Raised issue of runaway orbital pollution.
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\item \cite{Adilov2015}: Described 2 period salop model of interactions.
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\item \cite{Adilov2018,Adilov2018a}: Described an infinite period model with symmetric competitive interactions.
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\item \cite{RaoRondina2020}: Describe a symetric infinite period model (first to do so).
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\item \cite{Rao2020}: Examine the effect of Orbital-Use fees, find it would quadruple long term value produced of the space industry.
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\end{enumerate}
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\end{frame}
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%-------------------------------
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%-------------------------------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Model}
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%-------------------------------------------------------------------------------------
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\begin{frame}
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\frametitle{Overview}
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\begin{itemize}
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\item Mathematical Notation
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\item Law of motion for debris
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\item Law of motion for satellite stocks
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\item Kessler Syndrome
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\item Markov Decision Problems
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\end{itemize}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Mathematical Notation}
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\begin{itemize}
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\item $S_t$: The set of constellation satellites stocks.
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\item $s^i_t$: The number of satellites (stock) for constellation $i$.
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\item $D_t$: The level of debris.
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\item $X_t$: The set of launches.
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\item $x^i_t$: The launches from constellation $i$.
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\end{itemize}
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\end{frame}
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%-------------------------------
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%------------------------------------
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\subsection{Laws of Motion}
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%------------------------------------
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\begin{frame}
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\frametitle{Debris}
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Law of motion for debris
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\begin{align}
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D_{t+1} =& (1-\delta)D_t \tag{Debris decay.} \\
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&+ g\cdot D_t \tag{Debris produced by collision with debris.} \\
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&+ \gamma \sum^N_{i=1} \left(1-R^i(S_t,D_t) \right) s^i_t \tag{Debris produced by satellite destruction.} \\
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&+ \Gamma \sum^n_{j=1} x^j_t \tag{Debris produced by launches.}
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\end{align}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Satellite Stocks}
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Law of motion for satellite stocks
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\begin{align}
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s^i_{t+1} =& \left(
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R^i(S_t,D_t,X_t)
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- \eta
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\right) \cdot s^i_t
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+ x^i_t
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\end{align}
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\begin{itemize}
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\item $\eta$ is the orbit decay rate of satellites.
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\end{itemize}
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\end{frame}
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%-------------------------------
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%------------------------------------
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\subsection{Kessler Syndrome}
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%------------------------------------
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\begin{frame}
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\frametitle{Explanation of Kessler Syndrome}
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\begin{block}{Kessler Syndrome}
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The situation in which collisions between
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objects in orbit produced debris and this debris begins collisions
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with other objects, leading to a runaway growth in debris.
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As debris can persist for millenia, this may make some orbits unusable.
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\autocite{Kessler1978}
|
||||
\end{block}
|
||||
Often described as a condition with an exponential growth of debris.
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Past approaches to Kessler Syndrome}
|
||||
\begin{itemize}
|
||||
\item \cite{Adilov2018}:\\
|
||||
Develops an analog of kessler syndrome where the condition is met when satellites
|
||||
are destroyed immediately after launch by debris.
|
||||
\begin{align}
|
||||
\left\{ (S_t,D_t) : R^i(S_t,D_t) = 0 \forall i\right\}
|
||||
\end{align}
|
||||
\item \cite{RaoRondina2020}:\\
|
||||
A working paper in which the authors develop a dynamic model and a definition of
|
||||
kessler syndrome that captures all increasing debris levels.
|
||||
\begin{align}
|
||||
\left\{ (S_t,D_t) :
|
||||
\lim_{t \rightarrow \infty} D_{t+1}(S_t,D_t) = \infty
|
||||
\right\}
|
||||
\end{align}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{My contributions}
|
||||
I propose two refinements of these definitions to
|
||||
simplify analyzing kessler syndrome in computational models.
|
||||
\begin{itemize}
|
||||
\item $\epsilon$-Kessler Region
|
||||
\item Proto Kessler Region
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{$\epsilon$-Kessler Region}
|
||||
\begin{block}{$\epsilon$-Kessler Region}
|
||||
\begin{align}
|
||||
\kappa_\epsilon = \left\{ \left(S_t, D_t \right) : \forall k \geq 0,
|
||||
~~ D_{t+k+1} - D_{t+k} \geq \epsilon > 0 \right\}
|
||||
\end{align}
|
||||
\end{block}
|
||||
|
||||
Notable Features
|
||||
\begin{itemize}
|
||||
\item $\epsilon$ can be calibrated to capture only economically significant growth.
|
||||
\item Requires an explicit description of what is considered economically significant.
|
||||
\item Guarantees divergent behavior.
|
||||
\item Simulated transition paths can identify the region.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Proto Kessler Region}
|
||||
|
||||
\begin{block}{Proto Kessler Region}
|
||||
\begin{align}
|
||||
\kappa_\text{proto} =
|
||||
\left\{
|
||||
\left(S_t,D_t \right) : ~~ D_{t+1} - D_{t} \geq \epsilon_\text{proto}
|
||||
\right\}
|
||||
\end{align}
|
||||
\end{block}
|
||||
|
||||
Notable Features
|
||||
\begin{itemize}
|
||||
\item $\epsilon_\text{proto}$ can be calibrated to capture only economically significant growth.
|
||||
\item Requires an explicit description of what is considered economically significant.
|
||||
\item Does not guarantee divergent behavior.
|
||||
\item Easily computable kessler regions.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Proto Kessler Region}
|
||||
With the given law of motion for debris, the proto-kessler region is:
|
||||
\begin{align}
|
||||
\left\{
|
||||
\left(S_t,D_t \right) :
|
||||
(g-\delta) D_t
|
||||
+ \gamma \sum^n_{i=1} 1-R^i(S_t,D_t)
|
||||
+ \Gamma \sum^n_{i=1} x^i_t(S_t,D_t)
|
||||
\geq \epsilon_\text{proto}
|
||||
\right\}
|
||||
\end{align}
|
||||
\end{frame}
|
||||
%------------------------------------
|
||||
\subsection{Markov Decision Problem Formulation}
|
||||
%------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Operator's Problem}
|
||||
\begin{align}
|
||||
V^i(S_t, x^{\sim i}_t, D_t) = \max_{x^i_t} u^i(S_t, D_t) -F(x^i_t)
|
||||
+ \beta \left[ V^i(S_{t+1}, x^{\sim i}_{t+1}, D_{t+1}) \right]
|
||||
\end{align}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Benefit Functions}
|
||||
|
||||
Possible benefit functions
|
||||
\begin{itemize}
|
||||
\item Linear (Currently working on this one)
|
||||
\item Cournot Profits
|
||||
\item Profits under Partial substitutability
|
||||
\item Military capabilities (Keeping up with the Jones')
|
||||
\end{itemize}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Planner's Problem}
|
||||
\begin{align}
|
||||
W(S_t, D_t) =& \max_{X_t} \left[
|
||||
\sum^N_{i=1} \left(u^i(S_t, D_t) - F(x^i_t) \right)
|
||||
+ \beta \left[ W(S_{t+1}, D_{t+1}) \right]\right] \notag \\
|
||||
&\text{subject to:} \notag \\
|
||||
& s^i_{t+1} = (R^i(S_t, D_t)) s^i_t +x^i_t ~~~ \forall i \notag \\
|
||||
& D_{t+1} = (1-\delta + g)D_t
|
||||
+ \gamma \sum^N_{i=1} \left(1-R^i(\vec s_t, D_t)\right) s^i_t
|
||||
+ \Gamma \sum^N_{i=1} x^i_t
|
||||
\end{align}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Planned model expansions}
|
||||
\begin{itemize}
|
||||
\item Multiple interacting orbital shells and debris terms.
|
||||
\item Stochastic laws of motion
|
||||
\item Multiple types of operators
|
||||
\item Operators benefit functions include taxation
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Analysis}
|
||||
%-------------------------------------------------------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Issues}
|
||||
The following issues characterize the Operators' and Planner's problem
|
||||
\begin{itemize}
|
||||
\item Curse of Dimensionality
|
||||
\item Strategic Interaction (operators only)
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Possible approaches}
|
||||
|
||||
Possible approaches
|
||||
\begin{itemize}
|
||||
\item Standard VFI/Howards algorithm.
|
||||
\item VFI with sparse state space (dimensionality reduction).
|
||||
\item Reinforcement Learning.
|
||||
\item \cite{MALIAR2018} approaches using machine learning.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Chosen approach}
|
||||
% maliar et al - Bellman Residuals
|
||||
% present basic approach (using my notation)
|
||||
% Discuss basic training loop (use sutton and bartos term Generalized Policy Iteration)
|
||||
|
||||
Bellman Residual minimization due to \autocite{MALIAR2018}
|
||||
|
||||
Use NN to approximate $V(S_t,D_t|\theta_1)$ and $X(S_t,D_t|\theta_2)$.
|
||||
|
||||
The loss function is:
|
||||
\begin{align}
|
||||
0 =& \left[
|
||||
V(S_t, D_t) - F(S_t, D_t, X_t)- \beta V(S_{t+1}, D_{t+1})
|
||||
\right]^2 \notag\\
|
||||
&- v \left[
|
||||
F(S_t, D_t, X_t) + \beta V(S_{t+1}, D_{t+1})
|
||||
\right] \\
|
||||
0 =& \left[
|
||||
V(S_t, D_t) - F(S_t, D_t, X_t)- \beta V(S_{t+1}, D_{t+1})
|
||||
- \frac{v}{2}
|
||||
\right]^2
|
||||
- v \left[
|
||||
V(S_{t}, D_{t}) + \frac{v}{4}
|
||||
\right]
|
||||
\end{align}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Training Loop: Planner}
|
||||
|
||||
For each training epoch
|
||||
\begin{enumerate}
|
||||
\item Draw random data
|
||||
\item train policy function
|
||||
\item train value function
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Training Loop: Operators}
|
||||
|
||||
For each training epoch
|
||||
\begin{enumerate}
|
||||
\item Draw random data
|
||||
\item For each operator
|
||||
\begin{enumerate}
|
||||
\item train policy function
|
||||
\item train value function
|
||||
\end{enumerate}
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
%------------------------------------
|
||||
\subsection{Analysis so far}
|
||||
%------------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{State of the Code}
|
||||
Currently functioning
|
||||
\begin{itemize}
|
||||
\item Planner Value and Policy training
|
||||
\end{itemize}
|
||||
|
||||
|
||||
Almost functioning
|
||||
\begin{itemize}
|
||||
\item Operator Value and Policy training
|
||||
\item Proto-Kessler Region analysis
|
||||
\end{itemize}
|
||||
%Planner training
|
||||
%Operator training
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Results}
|
||||
%simulated debris paths (increase the ammount of debris a couple orders of magnitude)
|
||||
%Protokessler region plots?
|
||||
|
||||
Results are currently waiting on finishing the code.
|
||||
|
||||
\vspace{12pt}
|
||||
|
||||
Some analyses I plan on completing include
|
||||
\begin{itemize}
|
||||
\item Kessler Region analysis
|
||||
\item Free Entry conditions analysis
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Developing the Model%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Conclusion}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Summary}
|
||||
Summary
|
||||
\begin{enumerate}
|
||||
\item Created Dynamic model of the MDP facing satellite operators.
|
||||
\item Defined new Kessler Regions for computational analysis.
|
||||
\item Currently developing solution and simulation tools.
|
||||
\item Much work left to do.
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Other Areas Needing Work}
|
||||
|
||||
Related Orbits Work
|
||||
\begin{enumerate}
|
||||
\item Adding stochastic elements to the model.
|
||||
\item Parameter Estimation.
|
||||
\item Rights of Way.
|
||||
\item Satellite Lifetimes and constellation management.
|
||||
\end{enumerate}
|
||||
|
||||
Related computational work
|
||||
\begin{enumerate}
|
||||
\item Automating the Euler Equation Residuals method.
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Questions?}
|
||||
|
||||
\center
|
||||
Any remaining questions?
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}[allowframebreaks]
|
||||
\frametitle{References}
|
||||
\printbibliography
|
||||
\end{frame}
|
||||
%\begin{frame}
|
||||
% \frametitle{MarginalRevenue}
|
||||
% \begin{figure}
|
||||
% \tikzfig{../Assets/owned/ch8_MarginalRevenue}
|
||||
% \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg}
|
||||
% \label{FIG:costs}
|
||||
% \caption{Average Cost Curve as firms enter.}
|
||||
% \end{figure}
|
||||
%\end{frame}
|
||||
\end{document}
|
||||
% \begin{frame}
|
||||
% \frametitle{Columns}
|
||||
% \begin{columns}
|
||||
% \begin{column}{0.5\textwidth}
|
||||
% \end{column}
|
||||
% \begin{column}{0.5\textwidth}
|
||||
% \begin{figure}
|
||||
% \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2}
|
||||
% \label{FIG:costs}
|
||||
% \caption{Setting the Stage}
|
||||
% \end{figure}
|
||||
% \end{column}
|
||||
% \end{columns}
|
||||
% \end{frame}
|
||||
% %---------------------------------------------------------------
|
||||
@ -0,0 +1,42 @@
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{backgrounds}
|
||||
\usetikzlibrary{arrows}
|
||||
\usetikzlibrary{shapes,shapes.geometric,shapes.misc}
|
||||
|
||||
% this style is applied by default to any tikzpicture included via \tikzfig
|
||||
\tikzstyle{tikzfig}=[baseline=-0.25em,scale=0.5]
|
||||
|
||||
% these are dummy properties used by TikZiT, but ignored by LaTex
|
||||
\pgfkeys{/tikz/tikzit fill/.initial=0}
|
||||
\pgfkeys{/tikz/tikzit draw/.initial=0}
|
||||
\pgfkeys{/tikz/tikzit shape/.initial=0}
|
||||
\pgfkeys{/tikz/tikzit category/.initial=0}
|
||||
|
||||
% standard layers used in .tikz files
|
||||
\pgfdeclarelayer{edgelayer}
|
||||
\pgfdeclarelayer{nodelayer}
|
||||
\pgfsetlayers{background,edgelayer,nodelayer,main}
|
||||
|
||||
% style for blank nodes
|
||||
\tikzstyle{none}=[inner sep=0mm]
|
||||
|
||||
% include a .tikz file
|
||||
\newcommand{\tikzfig}[1]{%
|
||||
{\tikzstyle{every picture}=[tikzfig]
|
||||
\IfFileExists{#1.tikz}
|
||||
{\input{#1.tikz}}
|
||||
{%
|
||||
\IfFileExists{./figures/#1.tikz}
|
||||
{\input{./figures/#1.tikz}}
|
||||
{\tikz[baseline=-0.5em]{\node[draw=red,font=\color{red},fill=red!10!white] {\textit{#1}};}}%
|
||||
}}%
|
||||
}
|
||||
|
||||
% the same as \tikzfig, but in a {center} environment
|
||||
\newcommand{\ctikzfig}[1]{%
|
||||
\begin{center}\rm
|
||||
\tikzfig{#1}
|
||||
\end{center}}
|
||||
|
||||
% fix strange self-loops, which are PGF/TikZ default
|
||||
\tikzstyle{every loop}=[]
|
||||
@ -0,0 +1,27 @@
|
||||
|
||||
utline
|
||||
|
||||
Tell story
|
||||
- Why do we care? Kessler syndrome.
|
||||
- Why is space access needed? (satellite internet, GPS, military, hobbies, science, R&D, etc.)
|
||||
- Why now? (cubesats, lower launch costs, massive expansion in who launches, etc.)
|
||||
|
||||
|
||||
Present past models
|
||||
-
|
||||
-
|
||||
-
|
||||
|
||||
Present Current model
|
||||
-
|
||||
-
|
||||
-
|
||||
|
||||
|
||||
Present work on solving models.
|
||||
-
|
||||
-
|
||||
-
|
||||
|
||||
|
||||
Future work
|
||||
@ -0,0 +1,86 @@
|
||||
# Intro
|
||||
|
||||
Why do we care
|
||||
|
||||
Possible stories:
|
||||
sep 2019
|
||||
2020 - 3 near misses with ISS (https://www.jpost.com/science/international-space-station-nearly-struck-by-chinese-satellite-debris-684809)
|
||||
(https://orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv24i3.pdf)
|
||||
May 2020 - Fregat tank breakup (left debris from 1000 to 6000 miles in altitude)
|
||||
May 2021 - Canadarm2 got hit (https://www.asc-csa.gc.ca/eng/iss/news.asp, part way down)
|
||||
Nov 2021 - Dodge debris from anti-satellite test in 2007 (China) (Jerusalem post above)
|
||||
Nasa releases a
|
||||
Monday Nov 15, 2021 - ISS astronauts have to shelter in their exit craft due to a debris cloud nearing the ISS. (https://www.space.com/space-debris-astronauts-shelter-november-2021) (https://www.youtube.com/watch?v=m-LIh0fdfq8)
|
||||
- from youtube: limits the set of experiments they can work with.
|
||||
|
||||
Maybe explain the whole section.
|
||||
|
||||
Why should we care?
|
||||
- All orbits are subject to some degree of polution.
|
||||
- Common uses: GPS, Military Communications, Commercial internet and TV.
|
||||
- Exploratory uses: R&D of pharmaceuticals, exploration.
|
||||
- Collisions and debris damage are to some degree inevitable.
|
||||
- Kessler Syndrome
|
||||
|
||||
What is different now:
|
||||
- Launch costs (https://aerospace.csis.org/data/space-launch-to-low-earth-orbit-how-much-does-it-cost/) (https://fortune.com/2017/06/17/spacex-launch-cost-competition/)
|
||||
- Cubesats/nanosats (numbers at https://www.nanosats.eu/)
|
||||
- in short, accessability. With lower cost per mass to orbit, more reasons to go. With lower development costs, easier to build many small satellites. This gives us a need for urgency.
|
||||
- Anti-Satellite missles (US, RU, CH all have capability)
|
||||
- Starlink vs Kupiter vs OneWeb (UK gov)
|
||||
|
||||
# Present previous literature
|
||||
|
||||
Rao Rondina
|
||||
- Major results: exploitation of common pool resource
|
||||
Adilov et al
|
||||
- Major results: Exploitation of common pool resource
|
||||
Adilov et al
|
||||
- Major results: Divergence between economic and non-economic kessler syndromes
|
||||
|
||||
# my model
|
||||
- Kessler Syndrome work
|
||||
- Model description
|
||||
|
||||
# Solution methods
|
||||
- Issues
|
||||
- High dimensionality
|
||||
- Many Firms, Governments, and other organizations (How many different operators currently?)
|
||||
- Interacting debris fields between orbits (see the Fregat breakup)
|
||||
- Approximation is required
|
||||
- state space discretization
|
||||
- Not sure which states to examine
|
||||
- fuctional approximation
|
||||
- Maliar
|
||||
- Reinforcemnt learning
|
||||
- Choice of using NN approach
|
||||
- Well supported on hardware
|
||||
- Transfer learning
|
||||
-
|
||||
|
||||
|
||||
|
||||
# Analysis
|
||||
|
||||
# major points
|
||||
- Summaries of results so far.
|
||||
- Request for suggestions on utility functions that might be worth investigating
|
||||
- Discussion of goals
|
||||
- Investigate pigouvian taxation, cleanup bonds, etc.
|
||||
- Standardize interface so it is easy to estimate results.
|
||||
-
|
||||
- Discussion of other work that should happen
|
||||
- Estimation of parameters (simulation, bayesian, calibration, best guesstimates, etc)
|
||||
- Rights of way work (way to get operators to declare a no-move value?)
|
||||
- Satellite Lifetime Management and it's impact on decision making. (nested overlapping generations?)
|
||||
|
||||
Other sources
|
||||
Historical breakup events: https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv23i1.pdf
|
||||
Breakups: https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/pdfs/odqnv25i1.pdf
|
||||
Newsletter on debris breakups: https://www.orbitaldebris.jsc.nasa.gov/quarterly-news/
|
||||
|
||||
|
||||
remaining todo
|
||||
- Review planned model expansion
|
||||
- Reformulate bellman residual minimization to use Q and M
|
||||
- Get code working, and run a basic analysis (proto kessler regions)
|
||||
@ -0,0 +1,34 @@
|
||||
# Things I have learned about PyTorch and Neural networks.
|
||||
|
||||
## Building models
|
||||
All model building in Pytorch is based on the following three steps
|
||||
1. start by creating an object that extends the nn.Module base class
|
||||
1. define layers as class attributes (sequential wrapper for ease of use)
|
||||
2. implement the `.forward()` method
|
||||
|
||||
Each layer is just a predefined 'function'.
|
||||
Really, they are objects that extend the nn.Module base class.
|
||||
Thus each NN can act as a layer in another NN.
|
||||
For example, I reimplemented an upscaling layer in BasicNeuralNet2.
|
||||
(I picked up a lot of this info here.)[https://deeplizard.com/learn/video/k4jY9L8H89U]
|
||||
|
||||
|
||||
Also, neural networks can return more than just a single output as long as the
|
||||
loss function that is used for optimization can consume both of them.
|
||||
Thus I could write two separate neural networks (such as for launch and partials),
|
||||
and then write a third NN that binds the two together.
|
||||
|
||||
|
||||
## Notes on functions
|
||||
ReLU is a linear rectifier, it does not have any training involved.
|
||||
This makes it good for working as a final cleanup of the launch function.
|
||||
This also makes it not so good for the partial derivatives.
|
||||
|
||||
Linear is a good but basic network type.
|
||||
|
||||
Upscaling allows you to create more features.
|
||||
Downscaling reduces the number of features (by throwing data away?).
|
||||
Instead of downscaling, use a linear function to change the dimensions.
|
||||
|
||||
# Remaining Questions
|
||||
- How do you set it up to run over a set of variables, i.e. batches?
|
||||
@ -0,0 +1,208 @@
|
||||
import torch
|
||||
from torch.autograd.functional import jacobian
|
||||
import itertools
|
||||
import math
|
||||
import abc
|
||||
|
||||
|
||||
class EstimandInterface():
|
||||
"""
|
||||
This defines a clean interface for working with the estimand (i.e. thing we are trying to estimate).
|
||||
In general, we are trying to estimate the choice variables and the partial derivatives of the value functions.
|
||||
This
|
||||
|
||||
This class wraps output for the neural network (or other estimand), allowing me to
|
||||
- easily substitute various types of launch functions by having a common interface
|
||||
- this eases testing
|
||||
- check dimensionality etc without dealing with randomness
|
||||
- again, easing testing
|
||||
- reason more cleanly about the component pieces
|
||||
- easing programming
|
||||
- provide a clean interface to find constellation level launch decisions etc.
|
||||
|
||||
It takes inputs of two general categories:
|
||||
- the choice function results
|
||||
- the partial derivatives of the value function
|
||||
"""
|
||||
def __init__(self, partials, choices, deorbits=None):
|
||||
self.partials = partials
|
||||
self.choices = choices
|
||||
|
||||
@property
|
||||
def number_constellations(self):
|
||||
pass #fix this
|
||||
return self.choices.shape[-1]
|
||||
@property
|
||||
def number_states(self):
|
||||
pass #fix this
|
||||
return self.partials.shape[-1] #This depends on the debris trackers technically.
|
||||
|
||||
def choice_single(self, constellation):
|
||||
#returns the launch decision for the constellation of interest
|
||||
|
||||
filter_tensor = torch.zeros(self.number_constellations)
|
||||
filter_tensor[constellation] = 1.0
|
||||
|
||||
return self.choices @ filter_tensor
|
||||
|
||||
def choice_vector(self, constellation):
|
||||
#returns the launch decision for the constellation of interest as a vector
|
||||
|
||||
filter_tensor = torch.zeros(self.number_constellations)
|
||||
filter_tensor[constellation] = 1.0
|
||||
|
||||
return self.choices * filter_tensor
|
||||
|
||||
def partial_vector(self, constellation):
|
||||
#returns the partials of the value function corresponding to the constellation of interest
|
||||
|
||||
filter_tensor = torch.zeros(self.number_states)
|
||||
filter_tensor[constellation] = 1.0
|
||||
|
||||
return self.partials @ filter_tensor
|
||||
|
||||
def partial_matrix(self, constellation):
|
||||
#returns the partials of the value function corresponding to
|
||||
#the constellation of interest as a matrix
|
||||
|
||||
filter_tensor = torch.zeros(self.number_states)
|
||||
filter_tensor[constellation] = 1.0
|
||||
|
||||
return self.partials * filter_tensor
|
||||
|
||||
def __str__(self):
|
||||
#just a human readable descriptor
|
||||
return "Launch Decisions and Partial Derivativs of value function with\n\tlaunches\n\t\t {}\n\tPartials\n\t\t{}".format(self.choices,self.partials)
|
||||
|
||||
|
||||
class ChoiceFunction(torch.nn.Module):
|
||||
"""
|
||||
This is used to estimate the launch function
|
||||
"""
|
||||
def __init__(self
|
||||
,batch_size
|
||||
,number_states
|
||||
,number_choices
|
||||
,number_constellations
|
||||
,layer_size=12
|
||||
):
|
||||
super().__init__()
|
||||
|
||||
#preprocess
|
||||
self.preprocess = torch.nn.Linear(in_features=number_states, out_features=layer_size)
|
||||
|
||||
#upsample
|
||||
self.upsample = lambda x: torch.nn.Upsample(scale_factor=number_constellations)(x).view(batch_size
|
||||
,number_constellations
|
||||
,layer_size)
|
||||
|
||||
self.relu = torch.nn.ReLU() #used for coersion to the state space we care about.
|
||||
|
||||
|
||||
#sequential steps
|
||||
self.sequential = torch.nn.Sequential(
|
||||
torch.nn.Linear(in_features=layer_size, out_features=layer_size)
|
||||
#who knows if a convolution might help here.
|
||||
,torch.nn.Linear(in_features=layer_size, out_features=layer_size)
|
||||
,torch.nn.Linear(in_features=layer_size, out_features=layer_size)
|
||||
)
|
||||
|
||||
#reduce the feature axis to match expected results
|
||||
self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_choices)
|
||||
|
||||
|
||||
def forward(self, input_values):
|
||||
|
||||
intermediate_values = self.relu(input_values) #states should be positive anyway.
|
||||
|
||||
intermediate_values = self.preprocess(intermediate_values)
|
||||
intermediate_values = self.upsample(intermediate_values)
|
||||
intermediate_values = self.sequential(intermediate_values)
|
||||
intermediate_values = self.feature_reduction(intermediate_values)
|
||||
|
||||
intermediate_values = self.relu(intermediate_values) #launches are always positive, this may need removed for other types of choices.
|
||||
|
||||
return intermediate_values
|
||||
|
||||
class PartialDerivativesOfValueEstimand(torch.nn.Module):
|
||||
"""
|
||||
This is used to estimate the partial derivatives of the value functions
|
||||
"""
|
||||
def __init__(self
|
||||
,batch_size
|
||||
,number_constellations
|
||||
,number_states
|
||||
,layer_size=12):
|
||||
super().__init__()
|
||||
self.batch_size = batch_size #used for upscaling
|
||||
self.number_constellations = number_constellations
|
||||
self.number_states = number_states
|
||||
self.layer_size = layer_size
|
||||
|
||||
|
||||
#preprocess (single linear layer in case there is anything that needs to happen to all states)
|
||||
self.preprocess = torch.nn.Sequential(
|
||||
torch.nn.ReLU() #cleanup as states must be positive
|
||||
,torch.nn.Linear(in_features = self.number_states, out_features=self.number_states)
|
||||
)
|
||||
|
||||
#upsample to get the basic dimensionality correct. From (batch,State) to (batch, constellation, state). Includes a reshape
|
||||
self.upsample = lambda x: torch.nn.Upsample(scale_factor=self.number_constellations)(x).view(self.batch_size
|
||||
,self.number_constellations
|
||||
,self.number_states)
|
||||
|
||||
#sequential steps
|
||||
self.sequential = torch.nn.Sequential(
|
||||
torch.nn.Linear(in_features=number_states, out_features=layer_size)
|
||||
#who knows if a convolution or other layer type might help here.
|
||||
,torch.nn.Linear(in_features=layer_size, out_features=layer_size)
|
||||
,torch.nn.Linear(in_features=layer_size, out_features=layer_size)
|
||||
)
|
||||
|
||||
#reduce the feature axis to match expected results
|
||||
self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_states)
|
||||
|
||||
def forward(self, states):
|
||||
#Note that the input values are just going to be the state variables
|
||||
#TODO:check that input values match the prepared dimension?
|
||||
|
||||
#preprocess
|
||||
intermediate = self.preprocess(states)
|
||||
|
||||
#upscale the input values
|
||||
intermediate = self.upsample(intermediate)
|
||||
|
||||
#intermediate processing
|
||||
intermediate = self.sequential(intermediate)
|
||||
|
||||
#reduce feature axis to match the expected number of partials
|
||||
intermediate = self.feature_reduction(intermediate)
|
||||
|
||||
|
||||
return intermediate
|
||||
|
||||
|
||||
class EstimandNN(torch.nn.Module):
|
||||
"""
|
||||
This neural network takes the current states as input values and returns both
|
||||
the partial derivatives of the value function and the launch function.
|
||||
"""
|
||||
def __init__(self
|
||||
,batch_size
|
||||
,number_states
|
||||
,number_choices
|
||||
,number_constellations
|
||||
,layer_size=12
|
||||
):
|
||||
super().__init__()
|
||||
|
||||
|
||||
self.partials_estimator = PartialDerivativesOfValueEstimand(batch_size, number_constellations, number_states, layer_size)
|
||||
self.launch_estimator = ChoiceFunction(batch_size, number_states, number_choices, number_constellations, layer_size)
|
||||
|
||||
def forward(self, input_values):
|
||||
pass
|
||||
partials = self.partials_estimator(input_values)
|
||||
launch = self.launch_estimator(input_values)
|
||||
|
||||
return EstimandInterface(partials,launch)
|
||||
@ -0,0 +1,203 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "working-peeing",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import torch"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "decimal-boundary",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The purpose of this notebook is to allow me to investigate proper shaping of inputs.\n",
|
||||
"\n",
|
||||
"Typically pytorch chooses a tensor specification\n",
|
||||
"$$\n",
|
||||
"(N, .*)\n",
|
||||
"$$\n",
|
||||
"where $N$ is the batch size.\n",
|
||||
"For example a Convolutional NN layer expects\n",
|
||||
"$$\n",
|
||||
" NCHW\n",
|
||||
"$$\n",
|
||||
"for BatchSize,ChannelSize,Height,Width.\n",
|
||||
"On the other hand, Linear expects\n",
|
||||
"$$\n",
|
||||
" N.*H\n",
|
||||
"$$\n",
|
||||
"for BatchSize,any number of other dimensions, in_features\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"id": "eligible-isolation",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"class PartialDerivativesEstimand(torch.nn.Module):\n",
|
||||
" def __init__(self,batch_size, number_constellations, number_states,scale_factor=4, layer_size=12):\n",
|
||||
" \"\"\"\n",
|
||||
" \n",
|
||||
" \"\"\"\n",
|
||||
" super().__init__()\n",
|
||||
" self.batch_size = batch_size\n",
|
||||
" self.number_constellations = number_constellations\n",
|
||||
" self.number_states = number_states\n",
|
||||
" self.scale_factor = scale_factor\n",
|
||||
" self.layer_size = layer_size\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" #preprocess (single linear layer in case there is anything that needs to happen to all states)\n",
|
||||
" self.preprocess = torch.nn.Sequential(\n",
|
||||
" torch.nn.ReLU() #cleanup as states must be positive\n",
|
||||
" ,torch.nn.Linear(in_features = self.number_states, out_features=self.number_states)\n",
|
||||
" )\n",
|
||||
" #upscale to get the basic dimensionality correct. From (batch,State) to (batch, constellation, state). Includes a reshape\n",
|
||||
" self.upsample = lambda x: torch.nn.Upsample(scale_factor=self.number_constellations)(x).view(self.batch_size\n",
|
||||
" ,self.number_constellations\n",
|
||||
" ,self.number_states)\n",
|
||||
" \n",
|
||||
" #sequential steps\n",
|
||||
" self.sequential = torch.nn.Sequential(\n",
|
||||
" torch.nn.Linear(in_features=number_states, out_features=layer_size)\n",
|
||||
" #who knows if a convolution might help here.\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" )\n",
|
||||
"\n",
|
||||
" #reduce axis to match expectation\n",
|
||||
" self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_states)\n",
|
||||
" \n",
|
||||
" def forward(self, input_values):\n",
|
||||
" #Note that the input values are just going to be the state variables\n",
|
||||
" #TODO:check that input values match the prepared dimension?\n",
|
||||
" \n",
|
||||
" #preprocess\n",
|
||||
" intermediate = self.preprocess(input_values)\n",
|
||||
" \n",
|
||||
" #upscale the input values\n",
|
||||
" intermediate = self.upsample(intermediate)\n",
|
||||
" \n",
|
||||
" #intermediate processing\n",
|
||||
" intermediate = self.sequential(intermediate)\n",
|
||||
" \n",
|
||||
" #reduce feature axis to match the expected number of partials\n",
|
||||
" intermediate = self.feature_reduction(intermediate)\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" return intermediate"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"id": "literary-desktop",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"batch_size = 2\n",
|
||||
"constellations = 2\n",
|
||||
"number_states = constellations+1\n",
|
||||
"\n",
|
||||
"#initialize the NN\n",
|
||||
"a = PartialDerivativesEstimand(batch_size,constellations,number_states,scale_factor=2)\n",
|
||||
"\n",
|
||||
"#example state\n",
|
||||
"s = torch.rand(size=(batch_size,1,number_states))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"id": "second-graduation",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[[0.9283, 0.9414, 0.3426]],\n",
|
||||
"\n",
|
||||
" [[0.1902, 0.0369, 0.4699]]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"s"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"id": "reliable-alberta",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[[-0.1991, 0.1335, 0.2821],\n",
|
||||
" [-0.3549, 0.0213, 0.2322]],\n",
|
||||
"\n",
|
||||
" [[-0.1701, 0.1557, 0.2954],\n",
|
||||
" [-0.3017, 0.0690, 0.2419]]], grad_fn=<AddBackward0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"a(s)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "horizontal-judges",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "instant-lindsay",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -0,0 +1,793 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "french-experiment",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import torch\n",
|
||||
"from torch.autograd.functional import jacobian\n",
|
||||
"import itertools\n",
|
||||
"import math\n",
|
||||
"import abc\n",
|
||||
"\n",
|
||||
"class EconomicAgent(metaclass=abc.ABCMeta):\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def period_benefit(self,state,estimand_interface):\n",
|
||||
" pass\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def _period_benefit(self):\n",
|
||||
" pass\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def period_benefit_jacobian_wrt_states(self):\n",
|
||||
" pass\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def _period_benefit_jacobian_wrt_states(self):\n",
|
||||
" pass\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def period_benefit_jacobian_wrt_launches(self):\n",
|
||||
" pass\n",
|
||||
" @abc.abstractmethod\n",
|
||||
" def _period_benefit_jacobian_wrt_launches(self):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
"class LinearProfit(EconomicAgent):\n",
|
||||
" \"\"\"\n",
|
||||
" The simplest type of profit function available.\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self, constellation_number, discount_factor, benefit_weight, launch_cost, deorbit_cost=0):\n",
|
||||
" #track which constellation this is.\n",
|
||||
" self.constellation_number = constellation_number\n",
|
||||
"\n",
|
||||
" #parameters describing the agent's situation\n",
|
||||
" self.discount_factor = discount_factor\n",
|
||||
" self.benefit_weights = benefit_weight\n",
|
||||
" self.launch_cost = launch_cost\n",
|
||||
" self.deorbit_cost = deorbit_cost\n",
|
||||
"\n",
|
||||
" def __str__(self):\n",
|
||||
" return \"LinearProfit\\n Benefit weights:\\t{}\\n launch cost:\\t{}\\n Deorbit cost:\\t{}\".format(self.benefit_weights, self.launch_cost, self.deorbit_cost)\n",
|
||||
"\n",
|
||||
" def period_benefit(self,state,estimand_interface):\n",
|
||||
" return self._period_benefit(state.stocks, state.debris, estimand_interface.choices)\n",
|
||||
" \n",
|
||||
" def _period_benefit(self,stocks,debris,choice):\n",
|
||||
" profits = self.benefit_weights @ stocks \\\n",
|
||||
" - self.launch_cost * choice[self.constellation_number] #\\ \n",
|
||||
" #- deorbit_cost @ deorbits[self.constellation_number]\n",
|
||||
" return profits\n",
|
||||
"\n",
|
||||
" def period_benefit_jacobian_wrt_states(self, states, estimand_interface):\n",
|
||||
" return self._period_benefit_jacobian_wrt_states(states.stocks, states.debris, estimand_interface.choices)\n",
|
||||
"\n",
|
||||
" def _period_benefit_jacobian_wrt_states(self, stocks, debris, launches):\n",
|
||||
" jac = jacobian(self._period_benefit, (stocks,debris,launches))\n",
|
||||
" return torch.cat((jac[0], jac[1]))\n",
|
||||
" \n",
|
||||
" def period_benefit_jacobian_wrt_launches(self, states, estimand_interface):\n",
|
||||
" return self._period_benefit_jacobian_wrt_launches(states.stocks, states.debris, estimand_interface.choices)\n",
|
||||
"\n",
|
||||
" def _period_benefit_jacobian_wrt_launches(self,stocks,debris,launches):\n",
|
||||
" jac = jacobian(self._period_benefit, (stocks,debris,launches))\n",
|
||||
" return jac[2]\n",
|
||||
"\n",
|
||||
"class States():\n",
|
||||
" \"\"\"\n",
|
||||
" This is supposed to capture the state variables of the model, to create a common interface \n",
|
||||
" when passing between functions.\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self, stocks,debris):\n",
|
||||
" self.stocks = stocks\n",
|
||||
" self.debris = debris\n",
|
||||
" \n",
|
||||
"\n",
|
||||
" def __str__(self):\n",
|
||||
" return \"stocks\\t{} \\ndebris\\t {}\".format(self.stocks,self.debris)\n",
|
||||
"\n",
|
||||
" @property\n",
|
||||
" def number_constellations(self):\n",
|
||||
" return len(self.stocks)\n",
|
||||
" @property\n",
|
||||
" def number_debris_trackers(self):\n",
|
||||
" return len(self.debris)\n",
|
||||
"\n",
|
||||
" \n",
|
||||
"class EstimandInterface():\n",
|
||||
" \"\"\"\n",
|
||||
" This defines a clean interface for working with the estimand (i.e. thing we are trying to estimate).\n",
|
||||
" In general, we are trying to estimate the choice variables and the partial derivatives of the value functions.\n",
|
||||
" This \n",
|
||||
"\n",
|
||||
" This class wraps output for the neural network (or other estimand), allowing me to \n",
|
||||
" - easily substitute various types of launch functions by having a common interface\n",
|
||||
" - this eases testing\n",
|
||||
" - check dimensionality etc without dealing with randomness\n",
|
||||
" - again, easing testing\n",
|
||||
" - reason more cleanly about the component pieces\n",
|
||||
" - easing programming\n",
|
||||
" - provide a clean interface to find constellation level launch decisions etc.\n",
|
||||
"\n",
|
||||
" It takes inputs of two general categories:\n",
|
||||
" - the choice function results\n",
|
||||
" - the partial derivatives of the value function\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self, partials, choices, deorbits=None):\n",
|
||||
" self.partials = partials\n",
|
||||
" self.choices = choices\n",
|
||||
" \n",
|
||||
" @property\n",
|
||||
" def number_constellations(self):\n",
|
||||
" pass #fix this\n",
|
||||
" return self.choices.shape[-1]\n",
|
||||
" @property\n",
|
||||
" def number_states(self):\n",
|
||||
" pass #fix this\n",
|
||||
" return self.partials.shape[-1] #This depends on the debris trackers technically.\n",
|
||||
"\n",
|
||||
" def choice_single(self, constellation):\n",
|
||||
" #returns the launch decision for the constellation of interest\n",
|
||||
" \n",
|
||||
" filter_tensor = torch.zeros(self.number_constellations)\n",
|
||||
" filter_tensor[constellation] = 1.0\n",
|
||||
" \n",
|
||||
" return self.choices @ filter_tensor\n",
|
||||
" \n",
|
||||
" def choice_vector(self, constellation):\n",
|
||||
" #returns the launch decision for the constellation of interest as a vector\n",
|
||||
" \n",
|
||||
" filter_tensor = torch.zeros(self.number_constellations)\n",
|
||||
" filter_tensor[constellation] = 1.0\n",
|
||||
" \n",
|
||||
" return self.choices * filter_tensor\n",
|
||||
" \n",
|
||||
" def partial_vector(self, constellation):\n",
|
||||
" #returns the partials of the value function corresponding to the constellation of interest\n",
|
||||
" \n",
|
||||
" filter_tensor = torch.zeros(self.number_states)\n",
|
||||
" filter_tensor[constellation] = 1.0\n",
|
||||
" \n",
|
||||
" return self.partials @ filter_tensor\n",
|
||||
" \n",
|
||||
" def partial_matrix(self, constellation):\n",
|
||||
" #returns the partials of the value function corresponding to \n",
|
||||
" #the constellation of interest as a matrix\n",
|
||||
" \n",
|
||||
" filter_tensor = torch.zeros(self.number_states)\n",
|
||||
" filter_tensor[constellation] = 1.0\n",
|
||||
" \n",
|
||||
" return self.partials * filter_tensor\n",
|
||||
" \n",
|
||||
" def __str__(self):\n",
|
||||
" #just a human readable descriptor\n",
|
||||
" return \"Launch Decisions and Partial Derivativs of value function with\\n\\tlaunches\\n\\t\\t {}\\n\\tPartials\\n\\t\\t{}\".format(self.choices,self.partials)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class ChoiceFunction(torch.nn.Module):\n",
|
||||
" \"\"\"\n",
|
||||
" This is used to estimate the launch function\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self\n",
|
||||
" ,batch_size\n",
|
||||
" ,number_states\n",
|
||||
" ,number_choices\n",
|
||||
" ,number_constellations\n",
|
||||
" ,layer_size=12\n",
|
||||
" ):\n",
|
||||
" super().__init__()\n",
|
||||
" \n",
|
||||
" #preprocess\n",
|
||||
" self.preprocess = torch.nn.Linear(in_features=number_states, out_features=layer_size)\n",
|
||||
" \n",
|
||||
" #upsample\n",
|
||||
" self.upsample = lambda x: torch.nn.Upsample(scale_factor=number_constellations)(x).view(batch_size\n",
|
||||
" ,number_constellations\n",
|
||||
" ,layer_size)\n",
|
||||
" \n",
|
||||
" self.relu = torch.nn.ReLU() #used for coersion to the state space we care about.\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" #sequential steps\n",
|
||||
" self.sequential = torch.nn.Sequential(\n",
|
||||
" torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" #who knows if a convolution might help here.\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" )\n",
|
||||
"\n",
|
||||
" #reduce the feature axis to match expected results\n",
|
||||
" self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_choices)\n",
|
||||
"\n",
|
||||
" \n",
|
||||
" def forward(self, input_values):\n",
|
||||
" \n",
|
||||
" intermediate_values = self.relu(input_values) #states should be positive anyway.\n",
|
||||
" \n",
|
||||
" intermediate_values = self.preprocess(intermediate_values)\n",
|
||||
" intermediate_values = self.upsample(intermediate_values)\n",
|
||||
" intermediate_values = self.sequential(intermediate_values)\n",
|
||||
" intermediate_values = self.feature_reduction(intermediate_values)\n",
|
||||
" \n",
|
||||
" intermediate_values = self.relu(intermediate_values) #launches are always positive, this may need removed for other types of choices.\n",
|
||||
" \n",
|
||||
" return intermediate_values\n",
|
||||
"\n",
|
||||
"class PartialDerivativesOfValueEstimand(torch.nn.Module):\n",
|
||||
" \"\"\"\n",
|
||||
" This is used to estimate the partial derivatives of the value functions\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self\n",
|
||||
" ,batch_size\n",
|
||||
" , number_constellations\n",
|
||||
" , number_states\n",
|
||||
" , layer_size=12):\n",
|
||||
" super().__init__()\n",
|
||||
" self.batch_size = batch_size #used for upscaling\n",
|
||||
" self.number_constellations = number_constellations\n",
|
||||
" self.number_states = number_states\n",
|
||||
" self.layer_size = layer_size\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" #preprocess (single linear layer in case there is anything that needs to happen to all states)\n",
|
||||
" self.preprocess = torch.nn.Sequential(\n",
|
||||
" torch.nn.ReLU() #cleanup as states must be positive\n",
|
||||
" ,torch.nn.Linear(in_features = self.number_states, out_features=self.number_states)\n",
|
||||
" )\n",
|
||||
" \n",
|
||||
" #upsample to get the basic dimensionality correct. From (batch,State) to (batch, constellation, state). Includes a reshape\n",
|
||||
" self.upsample = lambda x: torch.nn.Upsample(scale_factor=self.number_constellations)(x).view(self.batch_size\n",
|
||||
" ,self.number_constellations\n",
|
||||
" ,self.number_states)\n",
|
||||
" \n",
|
||||
" #sequential steps\n",
|
||||
" self.sequential = torch.nn.Sequential(\n",
|
||||
" torch.nn.Linear(in_features=number_states, out_features=layer_size)\n",
|
||||
" #who knows if a convolution or other layer type might help here.\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
|
||||
" )\n",
|
||||
"\n",
|
||||
" #reduce the feature axis to match expected results\n",
|
||||
" self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_states)\n",
|
||||
" \n",
|
||||
" def forward(self, states):\n",
|
||||
" #Note that the input values are just going to be the state variables\n",
|
||||
" #TODO:check that input values match the prepared dimension?\n",
|
||||
" \n",
|
||||
" #preprocess\n",
|
||||
" intermediate = self.preprocess(states)\n",
|
||||
" \n",
|
||||
" #upscale the input values\n",
|
||||
" intermediate = self.upsample(intermediate)\n",
|
||||
" \n",
|
||||
" #intermediate processing\n",
|
||||
" intermediate = self.sequential(intermediate)\n",
|
||||
" \n",
|
||||
" #reduce feature axis to match the expected number of partials\n",
|
||||
" intermediate = self.feature_reduction(intermediate)\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" return intermediate\n",
|
||||
" "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "suited-nothing",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"class EstimandNN(torch.nn.Module):\n",
|
||||
" \"\"\"\n",
|
||||
" This neural network takes the current states as input values and returns both\n",
|
||||
" the partial derivatives of the value function and the launch function.\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self\n",
|
||||
" ,batch_size\n",
|
||||
" ,number_states\n",
|
||||
" ,number_choices\n",
|
||||
" ,number_constellations\n",
|
||||
" ,layer_size=12\n",
|
||||
" ):\n",
|
||||
" super().__init__()\n",
|
||||
" \n",
|
||||
"\n",
|
||||
" self.partials_estimator = PartialDerivativesOfValueEstimand(batch_size, number_constellations, number_states, layer_size)\n",
|
||||
" self.launch_estimator = ChoiceFunction(batch_size, number_states, number_choices, number_constellations, layer_size)\n",
|
||||
" \n",
|
||||
" def forward(self, input_values):\n",
|
||||
" pass\n",
|
||||
" partials = self.partials_estimator(input_values)\n",
|
||||
" launch = self.launch_estimator(input_values)\n",
|
||||
" \n",
|
||||
" return EstimandInterface(partials,launch)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "recognized-story",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Testing\n",
|
||||
"\n",
|
||||
"Test if states can handle the dimensionality needed."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"id": "smart-association",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"batch_size,states,choices = 5,3,1\n",
|
||||
"constellations = states -1 #determined by debris tracking\n",
|
||||
"max_start_state = 100\n",
|
||||
"\n",
|
||||
"stocks_and_debris = torch.randint(max_start_state,(batch_size,1,states),dtype=torch.float32)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 84,
|
||||
"id": "unsigned-hungary",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"torch.Size([5, 1, 3])"
|
||||
]
|
||||
},
|
||||
"execution_count": 84,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"stocks_and_debris.size()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "regulated-conversation",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Launch Decisions and Partial Derivativs of value function with\n",
|
||||
"\tlaunches\n",
|
||||
"\t\t tensor([[[0.0000],\n",
|
||||
" [0.0000]],\n",
|
||||
"\n",
|
||||
" [[2.0907],\n",
|
||||
" [0.1053]],\n",
|
||||
"\n",
|
||||
" [[2.9730],\n",
|
||||
" [2.2000]],\n",
|
||||
"\n",
|
||||
" [[2.3975],\n",
|
||||
" [1.2877]],\n",
|
||||
"\n",
|
||||
" [[4.2107],\n",
|
||||
" [2.0752]]], grad_fn=<ReluBackward0>)\n",
|
||||
"\tPartials\n",
|
||||
"\t\ttensor([[[ 0.1939, 0.3954, 0.0730],\n",
|
||||
" [-0.9428, 0.6145, -0.9247]],\n",
|
||||
"\n",
|
||||
" [[ 1.1686, 3.0170, 0.3393],\n",
|
||||
" [-7.1474, 2.3495, -7.0566]],\n",
|
||||
"\n",
|
||||
" [[-2.0849, 3.0883, -3.3791],\n",
|
||||
" [-0.6664, 0.0361, -2.2530]],\n",
|
||||
"\n",
|
||||
" [[-0.7117, 2.5474, -1.6458],\n",
|
||||
" [-2.1937, 0.6897, -3.0382]],\n",
|
||||
"\n",
|
||||
" [[-1.0262, 4.5973, -2.6606],\n",
|
||||
" [-5.4307, 1.4510, -6.6972]]], grad_fn=<AddBackward0>)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"print(a := enn.forward(stocks_and_debris))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "rental-detection",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def lossb(a):\n",
|
||||
" #test loss function\n",
|
||||
" return (a**2).sum()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 30,
|
||||
"id": "mechanical-joshua",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"ch = ChoiceFunction(batch_size\n",
|
||||
" ,states\n",
|
||||
" ,choices\n",
|
||||
" ,constellations\n",
|
||||
" ,12)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"id": "charged-request",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"tensor(46.8100, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(82442.4219, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n",
|
||||
"tensor(0., grad_fn=<SumBackward0>)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[[0.],\n",
|
||||
" [0.]],\n",
|
||||
"\n",
|
||||
" [[0.],\n",
|
||||
" [0.]],\n",
|
||||
"\n",
|
||||
" [[0.],\n",
|
||||
" [0.]],\n",
|
||||
"\n",
|
||||
" [[0.],\n",
|
||||
" [0.]],\n",
|
||||
"\n",
|
||||
" [[0.],\n",
|
||||
" [0.]]], grad_fn=<ReluBackward0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer = torch.optim.SGD(ch.parameters(),lr=0.01)\n",
|
||||
"\n",
|
||||
"for i in range(10):\n",
|
||||
" #training loop\n",
|
||||
" optimizer.zero_grad()\n",
|
||||
"\n",
|
||||
" output = ch.forward(stocks_and_debris)\n",
|
||||
"\n",
|
||||
" l = lossb(output)\n",
|
||||
"\n",
|
||||
" l.backward()\n",
|
||||
"\n",
|
||||
" optimizer.step()\n",
|
||||
"\n",
|
||||
" print(l)\n",
|
||||
" \n",
|
||||
"\n",
|
||||
"ch.forward(stocks_and_debris)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 45,
|
||||
"id": "perceived-permit",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def lossc(a):\n",
|
||||
" #test loss function\n",
|
||||
" return (a**2).sum()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 53,
|
||||
"id": "atomic-variance",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pd = PartialDerivativesOfValueEstimand(\n",
|
||||
" batch_size\n",
|
||||
" ,constellations\n",
|
||||
" ,states\n",
|
||||
" ,12)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 74,
|
||||
"id": "biological-badge",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"tensor(1.9948e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(1.7427e-05, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(5.7993e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(2.9985e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(6.5281e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(7.8818e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(4.4327e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(1.1240e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(1.2478e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(3.5818e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(4.3732e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(2.7699e-06, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(8.9659e-07, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(5.7541e-07, grad_fn=<SumBackward0>)\n",
|
||||
"tensor(1.5010e-06, grad_fn=<SumBackward0>)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[[ 0.0002, -0.0002, -0.0003],\n",
|
||||
" [ 0.0001, -0.0003, -0.0002]],\n",
|
||||
"\n",
|
||||
" [[ 0.0002, -0.0003, -0.0003],\n",
|
||||
" [ 0.0003, -0.0004, -0.0002]],\n",
|
||||
"\n",
|
||||
" [[ 0.0002, -0.0003, -0.0003],\n",
|
||||
" [ 0.0002, -0.0003, -0.0003]],\n",
|
||||
"\n",
|
||||
" [[ 0.0002, -0.0002, -0.0004],\n",
|
||||
" [ 0.0003, -0.0003, -0.0003]],\n",
|
||||
"\n",
|
||||
" [[ 0.0003, -0.0003, -0.0002],\n",
|
||||
" [ 0.0003, -0.0003, -0.0002]]], grad_fn=<AddBackward0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 74,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer = torch.optim.Adam(pd.parameters(),lr=0.0001)\n",
|
||||
"\n",
|
||||
"for i in range(15):\n",
|
||||
" #training loop\n",
|
||||
" optimizer.zero_grad()\n",
|
||||
"\n",
|
||||
" output = pd.forward(stocks_and_debris)\n",
|
||||
"\n",
|
||||
" l = lossc(output)\n",
|
||||
"\n",
|
||||
" l.backward()\n",
|
||||
"\n",
|
||||
" optimizer.step()\n",
|
||||
"\n",
|
||||
" print(l)\n",
|
||||
" \n",
|
||||
"\n",
|
||||
"pd.forward(stocks_and_debris)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 78,
|
||||
"id": "compliant-johnson",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def lossa(a):\n",
|
||||
" #test loss function\n",
|
||||
" return (a.choices**2).sum() + (a.partials**2).sum()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 81,
|
||||
"id": "alive-potato",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"enn = EstimandNN(batch_size\n",
|
||||
" ,states\n",
|
||||
" ,choices\n",
|
||||
" ,constellations\n",
|
||||
" ,12)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 83,
|
||||
"id": "changed-instruction",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0 tensor(112.1970, grad_fn=<AddBackward0>)\n",
|
||||
"10 tensor(79.8152, grad_fn=<AddBackward0>)\n",
|
||||
"20 tensor(55.6422, grad_fn=<AddBackward0>)\n",
|
||||
"30 tensor(38.5636, grad_fn=<AddBackward0>)\n",
|
||||
"40 tensor(26.9156, grad_fn=<AddBackward0>)\n",
|
||||
"50 tensor(18.9986, grad_fn=<AddBackward0>)\n",
|
||||
"60 tensor(13.6606, grad_fn=<AddBackward0>)\n",
|
||||
"70 tensor(10.1881, grad_fn=<AddBackward0>)\n",
|
||||
"80 tensor(8.0395, grad_fn=<AddBackward0>)\n",
|
||||
"90 tensor(6.7618, grad_fn=<AddBackward0>)\n",
|
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"100 tensor(6.0101, grad_fn=<AddBackward0>)\n",
|
||||
"110 tensor(5.5517, grad_fn=<AddBackward0>)\n",
|
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"120 tensor(5.2434, grad_fn=<AddBackward0>)\n",
|
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"130 tensor(5.0054, grad_fn=<AddBackward0>)\n",
|
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"140 tensor(4.7988, grad_fn=<AddBackward0>)\n",
|
||||
"150 tensor(4.6069, grad_fn=<AddBackward0>)\n",
|
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"160 tensor(4.4235, grad_fn=<AddBackward0>)\n",
|
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"170 tensor(4.2468, grad_fn=<AddBackward0>)\n",
|
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"180 tensor(4.0763, grad_fn=<AddBackward0>)\n",
|
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"190 tensor(3.9117, grad_fn=<AddBackward0>)\n",
|
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"200 tensor(3.7532, grad_fn=<AddBackward0>)\n",
|
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"210 tensor(3.6005, grad_fn=<AddBackward0>)\n",
|
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"220 tensor(3.4535, grad_fn=<AddBackward0>)\n",
|
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"230 tensor(3.3121, grad_fn=<AddBackward0>)\n",
|
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"240 tensor(3.1761, grad_fn=<AddBackward0>)\n",
|
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"250 tensor(3.0454, grad_fn=<AddBackward0>)\n",
|
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"260 tensor(2.9198, grad_fn=<AddBackward0>)\n",
|
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"270 tensor(2.7991, grad_fn=<AddBackward0>)\n",
|
||||
"280 tensor(2.6832, grad_fn=<AddBackward0>)\n",
|
||||
"290 tensor(2.5720, grad_fn=<AddBackward0>)\n",
|
||||
"300 tensor(2.4653, grad_fn=<AddBackward0>)\n",
|
||||
"310 tensor(2.3629, grad_fn=<AddBackward0>)\n",
|
||||
"320 tensor(2.2646, grad_fn=<AddBackward0>)\n",
|
||||
"330 tensor(2.1704, grad_fn=<AddBackward0>)\n",
|
||||
"340 tensor(2.0800, grad_fn=<AddBackward0>)\n",
|
||||
"350 tensor(1.9933, grad_fn=<AddBackward0>)\n",
|
||||
"360 tensor(1.9103, grad_fn=<AddBackward0>)\n",
|
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"370 tensor(1.8306, grad_fn=<AddBackward0>)\n",
|
||||
"380 tensor(1.7543, grad_fn=<AddBackward0>)\n",
|
||||
"390 tensor(1.6812, grad_fn=<AddBackward0>)\n",
|
||||
"400 tensor(1.6111, grad_fn=<AddBackward0>)\n",
|
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"410 tensor(1.5440, grad_fn=<AddBackward0>)\n",
|
||||
"420 tensor(1.4797, grad_fn=<AddBackward0>)\n",
|
||||
"430 tensor(1.4180, grad_fn=<AddBackward0>)\n",
|
||||
"440 tensor(1.3590, grad_fn=<AddBackward0>)\n",
|
||||
"450 tensor(1.3025, grad_fn=<AddBackward0>)\n",
|
||||
"460 tensor(1.2484, grad_fn=<AddBackward0>)\n",
|
||||
"470 tensor(1.1965, grad_fn=<AddBackward0>)\n",
|
||||
"480 tensor(1.1469, grad_fn=<AddBackward0>)\n",
|
||||
"490 tensor(1.0994, grad_fn=<AddBackward0>)\n",
|
||||
"500 tensor(1.0540, grad_fn=<AddBackward0>)\n",
|
||||
"510 tensor(1.0104, grad_fn=<AddBackward0>)\n",
|
||||
"520 tensor(0.9688, grad_fn=<AddBackward0>)\n",
|
||||
"530 tensor(0.9290, grad_fn=<AddBackward0>)\n",
|
||||
"540 tensor(0.8908, grad_fn=<AddBackward0>)\n",
|
||||
"550 tensor(0.8544, grad_fn=<AddBackward0>)\n",
|
||||
"560 tensor(0.8195, grad_fn=<AddBackward0>)\n",
|
||||
"570 tensor(0.7861, grad_fn=<AddBackward0>)\n",
|
||||
"580 tensor(0.7542, grad_fn=<AddBackward0>)\n",
|
||||
"590 tensor(0.7237, grad_fn=<AddBackward0>)\n",
|
||||
"600 tensor(0.6945, grad_fn=<AddBackward0>)\n",
|
||||
"610 tensor(0.6667, grad_fn=<AddBackward0>)\n",
|
||||
"620 tensor(0.6400, grad_fn=<AddBackward0>)\n",
|
||||
"630 tensor(0.6146, grad_fn=<AddBackward0>)\n",
|
||||
"640 tensor(0.5903, grad_fn=<AddBackward0>)\n",
|
||||
"650 tensor(0.5671, grad_fn=<AddBackward0>)\n",
|
||||
"660 tensor(0.5449, grad_fn=<AddBackward0>)\n",
|
||||
"670 tensor(0.5237, grad_fn=<AddBackward0>)\n",
|
||||
"680 tensor(0.5035, grad_fn=<AddBackward0>)\n",
|
||||
"690 tensor(0.4842, grad_fn=<AddBackward0>)\n",
|
||||
"700 tensor(0.4658, grad_fn=<AddBackward0>)\n",
|
||||
"710 tensor(0.4482, grad_fn=<AddBackward0>)\n",
|
||||
"720 tensor(0.4315, grad_fn=<AddBackward0>)\n",
|
||||
"730 tensor(0.4155, grad_fn=<AddBackward0>)\n",
|
||||
"740 tensor(0.4002, grad_fn=<AddBackward0>)\n",
|
||||
"750 tensor(0.3857, grad_fn=<AddBackward0>)\n",
|
||||
"760 tensor(0.3718, grad_fn=<AddBackward0>)\n",
|
||||
"770 tensor(0.3586, grad_fn=<AddBackward0>)\n",
|
||||
"780 tensor(0.3460, grad_fn=<AddBackward0>)\n",
|
||||
"790 tensor(0.3340, grad_fn=<AddBackward0>)\n",
|
||||
"800 tensor(0.3226, grad_fn=<AddBackward0>)\n",
|
||||
"810 tensor(0.3117, grad_fn=<AddBackward0>)\n",
|
||||
"820 tensor(0.3013, grad_fn=<AddBackward0>)\n",
|
||||
"830 tensor(0.2914, grad_fn=<AddBackward0>)\n",
|
||||
"840 tensor(0.2820, grad_fn=<AddBackward0>)\n",
|
||||
"850 tensor(0.2730, grad_fn=<AddBackward0>)\n",
|
||||
"860 tensor(0.2645, grad_fn=<AddBackward0>)\n",
|
||||
"870 tensor(0.2564, grad_fn=<AddBackward0>)\n",
|
||||
"880 tensor(0.2486, grad_fn=<AddBackward0>)\n",
|
||||
"890 tensor(0.2413, grad_fn=<AddBackward0>)\n",
|
||||
"900 tensor(0.2342, grad_fn=<AddBackward0>)\n",
|
||||
"910 tensor(0.2276, grad_fn=<AddBackward0>)\n",
|
||||
"920 tensor(0.2212, grad_fn=<AddBackward0>)\n",
|
||||
"930 tensor(0.2151, grad_fn=<AddBackward0>)\n",
|
||||
"940 tensor(0.2094, grad_fn=<AddBackward0>)\n",
|
||||
"950 tensor(0.2039, grad_fn=<AddBackward0>)\n",
|
||||
"960 tensor(0.1986, grad_fn=<AddBackward0>)\n",
|
||||
"970 tensor(0.1936, grad_fn=<AddBackward0>)\n",
|
||||
"980 tensor(0.1889, grad_fn=<AddBackward0>)\n",
|
||||
"990 tensor(0.1844, grad_fn=<AddBackward0>)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<__main__.EstimandInterface at 0x7f85609fce20>"
|
||||
]
|
||||
},
|
||||
"execution_count": 83,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer = torch.optim.Adam(enn.parameters(),lr=0.0001) #note the use of enn in the optimizer\n",
|
||||
"\n",
|
||||
"for i in range(1000):\n",
|
||||
" #training loop\n",
|
||||
" optimizer.zero_grad()\n",
|
||||
"\n",
|
||||
" output = enn.forward(stocks_and_debris)\n",
|
||||
"\n",
|
||||
" l = lossa(output)\n",
|
||||
"\n",
|
||||
" l.backward()\n",
|
||||
"\n",
|
||||
" optimizer.step()\n",
|
||||
"\n",
|
||||
" if i%10==0:\n",
|
||||
" print(i, l)\n",
|
||||
" \n",
|
||||
"\n",
|
||||
"enn.forward(stocks_and_debris)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "proved-amsterdam",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -0,0 +1,239 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "standing-catch",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import torch\n",
|
||||
"from torch.autograd.functional import jacobian\n",
|
||||
"import itertools\n",
|
||||
"import math"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"id": "going-accident",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import combined as c"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "severe-employment",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So, this contains a bunch of initial tests of my abstractions. I eventually need to change these to assertions and package them."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"id": "ranking-family",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"#Instantiate some objects\n",
|
||||
"pm = c.PhysicalModel(1.0,1e-6,0.01,2.0,1e-8)\n",
|
||||
"s = c.States(torch.tensor([1.0,2,3]), torch.tensor([0.0]))\n",
|
||||
"lp = c.LinearProfit(0,0.95,torch.tensor([1.0,0,0]), 5)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"id": "premium-brisbane",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(tensor([-7.5676e+05, 2.8893e+05, 4.6783e+05, 1.5236e+00]),\n",
|
||||
" <combined.States at 0x7f31f0146c10>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"c.single_transition(pm,lp,s,est_int)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "raised-worthy",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-718920.5625, 274490.1562, 444444.6250])"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"minimand, iterated_partials, iterated_state = c.optimality(pm,lp,s,est_int)\n",
|
||||
"minimand"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "horizontal-insight",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-2285563., -2285557., -2285557.])"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"est_int2 = c.EstimandInterface(iterated_partials,torch.ones(3))\n",
|
||||
"\n",
|
||||
"minimand2, iterated_partials2, iterated_state2 = c.optimality(pm,lp,iterated_state,est_int2)\n",
|
||||
"minimand2"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"id": "automatic-builder",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-2405858.5000, -2405852.5000, -2405852.5000])"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"est_int3 = c.EstimandInterface(iterated_partials2,torch.ones(3))\n",
|
||||
"\n",
|
||||
"minimand3, iterated_partials3, iterated_state3 = c.optimality(pm,lp,iterated_state2,est_int3)\n",
|
||||
"minimand3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "changing-mainland",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So, this succesfylly let me link the two. I'm going to move to another notebook, clean up, and start integrating the system"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "assumed-midwest",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"model = DoubleNetwork(input_size = 5, output_size=5, layers_size=15)\n",
|
||||
"\n",
|
||||
"data_in = torch.tensor([1.5,2,3,4,5])\n",
|
||||
"\n",
|
||||
"data_in\n",
|
||||
"\n",
|
||||
"target = torch.zeros(5)\n",
|
||||
"\n",
|
||||
"def loss_fn2(output,target):\n",
|
||||
" return sum((output[1] +output[0] - target)**2)\n",
|
||||
" #could add a simplicity assumption i.e. l1 on parameters.\n",
|
||||
"\n",
|
||||
"#Prep Optimizer\n",
|
||||
"optimizer = torch.optim.SGD(model.parameters(),lr=0.01)\n",
|
||||
"\n",
|
||||
"for i in range(20):\n",
|
||||
" #training loop\n",
|
||||
" optimizer.zero_grad()\n",
|
||||
"\n",
|
||||
" output = model.forward(data_in)\n",
|
||||
" output\n",
|
||||
"\n",
|
||||
" l = loss_fn2(output, target)\n",
|
||||
"\n",
|
||||
" l.backward()\n",
|
||||
"\n",
|
||||
" optimizer.step()\n",
|
||||
"\n",
|
||||
" print(\"\\n\",l)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "surprising-fundamentals",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "parliamentary-delta",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "emotional-castle",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "substantial-exhibit",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -0,0 +1,383 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "pleasant-equation",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import torch\n",
|
||||
"from torch.autograd.functional import jacobian\n",
|
||||
"import itertools\n",
|
||||
"import math"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "moved-christian",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import combined as c"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "pressed-slope",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So, this contains a bunch of initial tests of my abstractions. I eventually need to change these to assertions and package them."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"id": "capable-equality",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"#Instantiate some objects\n",
|
||||
"pm = c.PhysicalModel(1.0,1e-6,0.01,2.0,1e-8)\n",
|
||||
"s = c.States(torch.tensor([1.0,2,3]), torch.tensor([0.0]))\n",
|
||||
"lp = c.LinearProfit(0,0.95,torch.tensor([1.0,0,0]), 5)\n",
|
||||
"est_int = c.EstimandInterface(torch.tensor([[1.0,2,3,2]\n",
|
||||
" ,[4,5,6,2]\n",
|
||||
" ,[7,8,9,2]\n",
|
||||
" ,[1,3,5,7]]\n",
|
||||
" ),torch.ones(3))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"id": "written-experience",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"stocks\ttensor([1., 2., 3.]) \n",
|
||||
"debris\t tensor([0.])\n",
|
||||
"3\n",
|
||||
"1\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#test State object \n",
|
||||
"print(s)\n",
|
||||
"print(s.number_constellations)\n",
|
||||
"print(s.number_debris_trackers)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"id": "twelve-arthur",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Launch Decisions and Partial Derivativs of value function with\n",
|
||||
"\tlaunches\n",
|
||||
"\t\t tensor([1., 1., 1.])\n",
|
||||
"\tPartials\n",
|
||||
"\t\ttensor([[1., 2., 3., 2.],\n",
|
||||
" [4., 5., 6., 2.],\n",
|
||||
" [7., 8., 9., 2.],\n",
|
||||
" [1., 3., 5., 7.]])\n",
|
||||
"tensor([1., 1., 1.]) tensor([[1., 2., 3., 2.],\n",
|
||||
" [4., 5., 6., 2.],\n",
|
||||
" [7., 8., 9., 2.],\n",
|
||||
" [1., 3., 5., 7.]])\n",
|
||||
"tensor(1.)\n",
|
||||
"tensor([0., 1., 0.])\n",
|
||||
"tensor([2., 5., 8., 3.])\n",
|
||||
"tensor([[0., 2., 0., 0.],\n",
|
||||
" [0., 5., 0., 0.],\n",
|
||||
" [0., 8., 0., 0.],\n",
|
||||
" [0., 3., 0., 0.]])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Test estimand interface\n",
|
||||
"print(est_int)\n",
|
||||
"print(est_int.launches,est_int.partials)\n",
|
||||
"\n",
|
||||
"print(est_int.launch_single(1))\n",
|
||||
"print(est_int.launch_vector(1))\n",
|
||||
"print(est_int.partial_vector(1)) \n",
|
||||
"print(est_int.partial_matrix(1)) #TODO: double check orientation"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "impressive-tribe",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"1.0\n",
|
||||
"1e-06\n",
|
||||
"0.01\n",
|
||||
"2.0\n",
|
||||
"1e-08\n",
|
||||
"tensor([1.0133e-06, 2.0266e-06, 2.9802e-06])\n",
|
||||
"tensor([1., 2., 3.]) tensor([0.])\n",
|
||||
"tensor([1.0000, 1.0000, 1.0000]) tensor([12.0000])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Test physical model methods\n",
|
||||
"print(pm)\n",
|
||||
"print(pm.survival(s))\n",
|
||||
"s2 = pm.transition(s,est_int)\n",
|
||||
"print(s.stocks,s.debris)\n",
|
||||
"print(s2.stocks,s2.debris)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "stretch-reward",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"LinearProfit\n",
|
||||
" Benefit weights:\ttensor([1., 0., 0.])\n",
|
||||
" launch cost:\t5\n",
|
||||
" Deorbit cost:\t0\n",
|
||||
"tensor(-4.)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#test linear profit object\n",
|
||||
"print(lp)\n",
|
||||
"print(lp.period_benefit(s,est_int))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"id": "advance-folder",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([1., 0., 0., 0.])"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"lp._period_benefit_jacobian_wrt_states( s.stocks, s.debris, est_int.launches)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"id": "posted-subscriber",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-5., 0., 0.])"
|
||||
]
|
||||
},
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"lp._period_benefit_jacobian_wrt_launches( s.stocks, s.debris, est_int.launches)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"id": "divine-agenda",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([1., 0., 0., 0.])"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"lp.period_benefit_jacobian_wrt_states( s, est_int)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"id": "surgical-direction",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[1., 2., 3., 2.],\n",
|
||||
" [4., 5., 6., 2.],\n",
|
||||
" [7., 8., 9., 2.],\n",
|
||||
" [1., 3., 5., 7.]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"est_int.partials"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"id": "mounted-roots",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(tensor([-7.5676e+05, 2.8893e+05, 4.6783e+05, 1.5236e+00]),\n",
|
||||
" <combined.States at 0x7f8c3c9c54f0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"c.single_transition(pm,lp,s,est_int)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"id": "pediatric-iceland",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-718920.5625, 274490.1562, 444444.6250])"
|
||||
]
|
||||
},
|
||||
"execution_count": 24,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"minimand, iterated_partials, iterated_state = c.optimality(pm,lp,s,est_int)\n",
|
||||
"minimand"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"id": "isolated-cleveland",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([-2285563., -2285557., -2285557.])"
|
||||
]
|
||||
},
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"est_int2 = c.EstimandInterface(iterated_partials,torch.ones(3))\n",
|
||||
"\n",
|
||||
"minimand2, iterated_partials2, iterated_state2 = c.optimality(pm,lp,iterated_state,est_int2)\n",
|
||||
"minimand2"
|
||||
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|
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"data": {
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|
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|
||||
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|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"est_int3 = c.EstimandInterface(iterated_partials2,torch.ones(3))\n",
|
||||
"\n",
|
||||
"minimand3, iterated_partials3, iterated_state3 = c.optimality(pm,lp,iterated_state2,est_int3)\n",
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||||
"minimand3"
|
||||
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|
||||
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|
||||
{
|
||||
"cell_type": "markdown",
|
||||
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|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So, this succesfylly let me link the two. I'm going to move to another notebook, clean up, and start integrating the system"
|
||||
]
|
||||
}
|
||||
],
|
||||
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|
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||||
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|
||||
}
|
||||
@ -0,0 +1,117 @@
|
||||
\documentclass{article}
|
||||
|
||||
%Setup Subfiles
|
||||
\usepackage{subfiles}
|
||||
|
||||
|
||||
|
||||
%Include preambles
|
||||
\input{assets/preambles/MathPreamble}
|
||||
%\input{assets/preambles/TikzitPreamble}
|
||||
\input{assets/preambles/BibPreamble}
|
||||
\input{assets/preambles/GeneralPreamble}
|
||||
|
||||
\title{Summary of my work on Satellite Constellations}
|
||||
\author{William King}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\section{Introduction}
|
||||
\subfile{sections/00_Introduction} %Currently from past semesters.
|
||||
%roughly done 2021-07-15
|
||||
|
||||
%Describe sections
|
||||
The paper is organized as follows.
|
||||
Section \ref{SEC:Models}, describes the laws of motion
|
||||
governing satellites and debris(\ref{SEC:Laws})%,
|
||||
%places limits on various measures of risk (\ref{SEC:Survival}),
|
||||
and reviews various definitions of kessler syndrome in
|
||||
the context of dynamic modeling, their advantages, and their disadvanteges (\ref{SEC:Kessler}).
|
||||
It then describes the dynamic problem faced by constellation operators
|
||||
(\ref{SEC:Operator}) and social planners (\ref{SEC:Planner}).
|
||||
Section \ref{SEC:Computation} describes the computational approach and the
|
||||
results are reported in \cref{SEC:Results}.
|
||||
Section \ref{SEC:Conclusion} concludes with a discussion of limitations, concerns,
|
||||
and remaining policy questions.
|
||||
|
||||
%\section{Modeling the Environment}\label{SEC:Environment}
|
||||
\section{Model}\label{SEC:Models}
|
||||
\subsection{Laws of motion}\label{SEC:Laws}
|
||||
\subfile{sections/01_LawsOfMotion} %Roughly done 2021-07-15
|
||||
|
||||
%\subsection{Marginal survival rates}\label{SEC:Survival}
|
||||
%\subfile{sections/03_SurvivalAnalysis} %roughly done 2021-07-14
|
||||
% Thoughts on removal: This doesn't add much to the actual questions.
|
||||
% It is interesting, but in a paper is just too much.
|
||||
% I'll keep it here to add it back easily.
|
||||
|
||||
\subsection{Kessler Syndrome}\label{SEC:Kessler}
|
||||
% Kessler syndrome follows laws of motion because it is the main
|
||||
% threat of orbital pollution and needs to be included.
|
||||
% Also, there is not really a better place to place it.
|
||||
\subfile{sections/02_KesslerSyndrome} %roughly done before 2021-07-14
|
||||
\subfile{sections/06_KesslerRegion} %roughly done before 2021-07-14
|
||||
|
||||
\subsection{Constellation Operator's Program}\label{SEC:Operator}
|
||||
\subfile{sections/04_ConstellationOperator} %Reasonably done.
|
||||
|
||||
\subsection{Social Planner's Program}\label{SEC:Planner}
|
||||
\subfile{sections/05_SocialPlanner} %Reasonably done?
|
||||
|
||||
\section{Computation}\label{SEC:Computation}
|
||||
\subfile{sections/07_ComputationalApproach} %needs some clarifications.
|
||||
|
||||
\section{Results}\label{SEC:Results}
|
||||
\subfile{sections/09_Results} %TODO
|
||||
|
||||
\section{Conclusion}\label{SEC:Conclusion}
|
||||
\subfile{sections/08_Conclusion} %TODO
|
||||
|
||||
|
||||
\newpage
|
||||
\section{References}
|
||||
\printbibliography
|
||||
\newpage
|
||||
\section{Appedicies}
|
||||
\subsection{Mathematical Notation}
|
||||
Needs completed.
|
||||
%\subsection{Deriving Marginal Survival Rates}\label{APX:Derivations:SurvivalRates}
|
||||
%\subfile{sections/apx_01_MarginalSurvivalRates}
|
||||
|
||||
\subsection{Deriving Euler Equations}\label{APX:Derivations:EulerEquations}
|
||||
\subfile{sections/apx_02_GeneralizedEuEqSteps}
|
||||
|
||||
|
||||
\subsection{Collected Assumptions and Caveats}\label{APX:CollectedAssumptions}
|
||||
I hope to write a section clearly explaining assumptions, caveats, and shortcomings here.
|
||||
These will later get written back into the other sections, but I want to collect them
|
||||
in a single place first.
|
||||
%time periods are long enough for debris to disperse after collisions.
|
||||
%Only a single type of debris
|
||||
%With my current computational idea; each constellation provides the same risk to each other constellation
|
||||
% That can be easily adjusted in the computational models.
|
||||
|
||||
\newpage
|
||||
%Just for simplicity, remove later
|
||||
\tableofcontents
|
||||
\end{document}
|
||||
|
||||
%%% Notes to keep track of
|
||||
% Possible other things to investigate
|
||||
% - Free-entry conditions: which of the following?
|
||||
% - When for every operator, the current stocks imply no more launches(x = 0).
|
||||
% - When for every type of operator, the current stocks plus an own stock of 0 imply no more launches(x = 0).
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
%
|
||||
@ -0,0 +1,13 @@
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File diff suppressed because it is too large
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File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
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git-tree-sha1 = "77d915a0af27d474f0aaf12fcd46c400a552e84c"
|
||||
uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
|
||||
version = "0.13.7"
|
||||
|
||||
[[IRTools]]
|
||||
deps = ["InteractiveUtils", "MacroTools", "Test"]
|
||||
git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
|
||||
uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
|
||||
version = "0.4.3"
|
||||
|
||||
[[IfElse]]
|
||||
git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
|
||||
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
|
||||
version = "0.1.1"
|
||||
|
||||
[[InteractiveUtils]]
|
||||
deps = ["Markdown"]
|
||||
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
|
||||
|
||||
[[InverseFunctions]]
|
||||
deps = ["Test"]
|
||||
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
|
||||
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
|
||||
version = "0.1.2"
|
||||
|
||||
[[IrrationalConstants]]
|
||||
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
|
||||
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
|
||||
version = "0.1.1"
|
||||
|
||||
[[JLLWrappers]]
|
||||
deps = ["Preferences"]
|
||||
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
|
||||
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
|
||||
version = "1.3.0"
|
||||
|
||||
[[Juno]]
|
||||
deps = ["Base64", "Logging", "Media", "Profile"]
|
||||
git-tree-sha1 = "07cb43290a840908a771552911a6274bc6c072c7"
|
||||
uuid = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
|
||||
version = "0.8.4"
|
||||
|
||||
[[LLVM]]
|
||||
deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
|
||||
git-tree-sha1 = "46092047ca4edc10720ecab437c42283cd7c44f3"
|
||||
uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
|
||||
version = "4.6.0"
|
||||
|
||||
[[LLVMExtra_jll]]
|
||||
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
|
||||
git-tree-sha1 = "9436f02a0c9f726d914cc6539f87850701be18fc"
|
||||
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
|
||||
version = "0.0.12+0"
|
||||
|
||||
[[LazyArtifacts]]
|
||||
deps = ["Artifacts", "Pkg"]
|
||||
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
|
||||
|
||||
[[LibCURL]]
|
||||
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
|
||||
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
|
||||
|
||||
[[LibCURL_jll]]
|
||||
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
|
||||
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
|
||||
|
||||
[[LibGit2]]
|
||||
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
|
||||
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
|
||||
|
||||
[[LibSSH2_jll]]
|
||||
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
|
||||
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
|
||||
|
||||
[[Libdl]]
|
||||
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
|
||||
|
||||
[[LinearAlgebra]]
|
||||
deps = ["Libdl"]
|
||||
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
|
||||
|
||||
[[LogExpFunctions]]
|
||||
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
|
||||
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
|
||||
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
|
||||
version = "0.3.5"
|
||||
|
||||
[[Logging]]
|
||||
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
|
||||
|
||||
[[MacroTools]]
|
||||
deps = ["Markdown", "Random"]
|
||||
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
|
||||
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
|
||||
version = "0.5.9"
|
||||
|
||||
[[Markdown]]
|
||||
deps = ["Base64"]
|
||||
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
|
||||
|
||||
[[MbedTLS_jll]]
|
||||
deps = ["Artifacts", "Libdl"]
|
||||
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
|
||||
|
||||
[[Media]]
|
||||
deps = ["MacroTools", "Test"]
|
||||
git-tree-sha1 = "75a54abd10709c01f1b86b84ec225d26e840ed58"
|
||||
uuid = "e89f7d12-3494-54d1-8411-f7d8b9ae1f27"
|
||||
version = "0.5.0"
|
||||
|
||||
[[Missings]]
|
||||
deps = ["DataAPI"]
|
||||
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
|
||||
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
|
||||
version = "1.0.2"
|
||||
|
||||
[[Mmap]]
|
||||
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
|
||||
|
||||
[[MozillaCACerts_jll]]
|
||||
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
|
||||
|
||||
[[NNlib]]
|
||||
deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
|
||||
git-tree-sha1 = "2eb305b13eaed91d7da14269bf17ce6664bfee3d"
|
||||
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
|
||||
version = "0.7.31"
|
||||
|
||||
[[NNlibCUDA]]
|
||||
deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
|
||||
git-tree-sha1 = "38358632d9c277f7bf8d202c127f601e8467aa4d"
|
||||
uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
|
||||
version = "0.1.10"
|
||||
|
||||
[[NaNMath]]
|
||||
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
|
||||
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
|
||||
version = "0.3.5"
|
||||
|
||||
[[NetworkOptions]]
|
||||
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
|
||||
|
||||
[[OpenLibm_jll]]
|
||||
deps = ["Artifacts", "Libdl"]
|
||||
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
|
||||
|
||||
[[OpenSpecFun_jll]]
|
||||
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
|
||||
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
|
||||
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
|
||||
version = "0.5.5+0"
|
||||
|
||||
[[OrderedCollections]]
|
||||
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
|
||||
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
|
||||
version = "1.4.1"
|
||||
|
||||
[[Pkg]]
|
||||
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
|
||||
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
|
||||
|
||||
[[Preferences]]
|
||||
deps = ["TOML"]
|
||||
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
|
||||
uuid = "21216c6a-2e73-6563-6e65-726566657250"
|
||||
version = "1.2.2"
|
||||
|
||||
[[Printf]]
|
||||
deps = ["Unicode"]
|
||||
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
|
||||
|
||||
[[Profile]]
|
||||
deps = ["Printf"]
|
||||
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
|
||||
|
||||
[[REPL]]
|
||||
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
|
||||
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
|
||||
|
||||
[[Random]]
|
||||
deps = ["Serialization"]
|
||||
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
|
||||
|
||||
[[Random123]]
|
||||
deps = ["Libdl", "Random", "RandomNumbers"]
|
||||
git-tree-sha1 = "0e8b146557ad1c6deb1367655e052276690e71a3"
|
||||
uuid = "74087812-796a-5b5d-8853-05524746bad3"
|
||||
version = "1.4.2"
|
||||
|
||||
[[RandomNumbers]]
|
||||
deps = ["Random", "Requires"]
|
||||
git-tree-sha1 = "043da614cc7e95c703498a491e2c21f58a2b8111"
|
||||
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
|
||||
version = "1.5.3"
|
||||
|
||||
[[RealDot]]
|
||||
deps = ["LinearAlgebra"]
|
||||
git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
|
||||
uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
|
||||
version = "0.1.0"
|
||||
|
||||
[[Reexport]]
|
||||
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
|
||||
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
|
||||
version = "1.2.2"
|
||||
|
||||
[[Requires]]
|
||||
deps = ["UUIDs"]
|
||||
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
|
||||
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
|
||||
version = "1.1.3"
|
||||
|
||||
[[SHA]]
|
||||
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
|
||||
|
||||
[[Serialization]]
|
||||
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
|
||||
|
||||
[[SharedArrays]]
|
||||
deps = ["Distributed", "Mmap", "Random", "Serialization"]
|
||||
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
|
||||
|
||||
[[Sockets]]
|
||||
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
|
||||
|
||||
[[SortingAlgorithms]]
|
||||
deps = ["DataStructures"]
|
||||
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
|
||||
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
|
||||
version = "1.0.1"
|
||||
|
||||
[[SparseArrays]]
|
||||
deps = ["LinearAlgebra", "Random"]
|
||||
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
|
||||
|
||||
[[SpecialFunctions]]
|
||||
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
|
||||
git-tree-sha1 = "f0bccf98e16759818ffc5d97ac3ebf87eb950150"
|
||||
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
|
||||
version = "1.8.1"
|
||||
|
||||
[[Static]]
|
||||
deps = ["IfElse"]
|
||||
git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
|
||||
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
|
||||
version = "0.4.0"
|
||||
|
||||
[[StaticArrays]]
|
||||
deps = ["LinearAlgebra", "Random", "Statistics"]
|
||||
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
|
||||
uuid = "90137ffa-7385-5640-81b9-e52037218182"
|
||||
version = "1.2.13"
|
||||
|
||||
[[Statistics]]
|
||||
deps = ["LinearAlgebra", "SparseArrays"]
|
||||
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
|
||||
|
||||
[[StatsAPI]]
|
||||
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
|
||||
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
|
||||
version = "1.0.0"
|
||||
|
||||
[[StatsBase]]
|
||||
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
|
||||
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
|
||||
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
|
||||
version = "0.33.13"
|
||||
|
||||
[[TOML]]
|
||||
deps = ["Dates"]
|
||||
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
|
||||
|
||||
[[Tar]]
|
||||
deps = ["ArgTools", "SHA"]
|
||||
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
|
||||
|
||||
[[Test]]
|
||||
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
|
||||
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
|
||||
|
||||
[[TimerOutputs]]
|
||||
deps = ["ExprTools", "Printf"]
|
||||
git-tree-sha1 = "7cb456f358e8f9d102a8b25e8dfedf58fa5689bc"
|
||||
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
|
||||
version = "0.5.13"
|
||||
|
||||
[[TranscodingStreams]]
|
||||
deps = ["Random", "Test"]
|
||||
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
|
||||
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
|
||||
version = "0.9.6"
|
||||
|
||||
[[UUIDs]]
|
||||
deps = ["Random", "SHA"]
|
||||
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
|
||||
|
||||
[[Unicode]]
|
||||
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
|
||||
|
||||
[[ZipFile]]
|
||||
deps = ["Libdl", "Printf", "Zlib_jll"]
|
||||
git-tree-sha1 = "3593e69e469d2111389a9bd06bac1f3d730ac6de"
|
||||
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
|
||||
version = "0.9.4"
|
||||
|
||||
[[Zlib_jll]]
|
||||
deps = ["Libdl"]
|
||||
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
|
||||
|
||||
[[Zygote]]
|
||||
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
|
||||
git-tree-sha1 = "2c30f2df0ba43c17e88c8b55b5b22c401f7cde4e"
|
||||
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
|
||||
version = "0.6.30"
|
||||
|
||||
[[ZygoteRules]]
|
||||
deps = ["MacroTools"]
|
||||
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
|
||||
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
|
||||
version = "0.2.2"
|
||||
|
||||
[[nghttp2_jll]]
|
||||
deps = ["Artifacts", "Libdl"]
|
||||
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
|
||||
|
||||
[[p7zip_jll]]
|
||||
deps = ["Artifacts", "Libdl"]
|
||||
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
|
||||
@ -0,0 +1,5 @@
|
||||
[deps]
|
||||
BSON = "fbb218c0-5317-5bc6-957e-2ee96dd4b1f0"
|
||||
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
|
||||
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
|
||||
Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
|
||||
@ -0,0 +1 @@
|
||||
Description goes here
|
||||
@ -0,0 +1,81 @@
|
||||
include("../src/Orbits.jl")
|
||||
using .Orbits
|
||||
using LinearAlgebra
|
||||
|
||||
#Set key dimensions
|
||||
const N_constellations = 4
|
||||
const N_debris = 1
|
||||
const N_states = N_constellations + N_debris
|
||||
|
||||
#Setup Economic Models
|
||||
em2_a = LinearModel(0.95, [1 -0.02 -0.02 0], [5.0 0 0 0])
|
||||
em2_b = LinearModel(0.95, [-0.02 1 -0.02 0], [0.0 5 0 0])
|
||||
em2_c = LinearModel(0.95, [0 -0.02 1 -0.02], [0.0 0 5 0])
|
||||
em2_d = LinearModel(0.95, [0 -0.02 -0.02 1], [0.0 0 0 5])
|
||||
|
||||
#Setup Physics
|
||||
|
||||
basic_model = BasicPhysics(
|
||||
0.002
|
||||
,0.002*(ones(N_constellations,N_constellations) - LinearAlgebra.I)
|
||||
,0.01
|
||||
,0.001
|
||||
,5.0
|
||||
,0.05
|
||||
)
|
||||
|
||||
# Setup NN
|
||||
bg = BranchGenerator(N_constellations)
|
||||
operators_policy = bg(operator_policy_function_generator(N_constellations,N_debris),vcat)
|
||||
planners_policy = bg(operator_policy_function_generator(N_constellations,N_debris),vcat)
|
||||
planners_value = value_function_generator(64)
|
||||
|
||||
|
||||
# Setup Operators
|
||||
const operator_array = [
|
||||
#first operator
|
||||
OperatorLoss(
|
||||
em2_a
|
||||
,value_function_generator()
|
||||
,operators_policy #this is held by all operators
|
||||
,params(operators_policy[2][1]) #first operator gets first branch of params
|
||||
,basic_model
|
||||
)
|
||||
,OperatorLoss(
|
||||
em2_b
|
||||
,value_function_generator()
|
||||
,operators_policy #this is held by all operators
|
||||
,params(operators_policy[2][2]) #first operator gets first branch of params
|
||||
,basic_model
|
||||
)
|
||||
,OperatorLoss(
|
||||
em2_c
|
||||
,value_function_generator()
|
||||
,operators_policy #this is held by all operators
|
||||
,params(operators_policy[2][3]) #first operator gets first branch of params
|
||||
,basic_model
|
||||
)
|
||||
,OperatorLoss(
|
||||
em2_d
|
||||
,value_function_generator()
|
||||
,operators_policy #this is held by all operators
|
||||
,params(operators_policy[2][4]) #first operator gets first branch of params
|
||||
,basic_model
|
||||
)
|
||||
]
|
||||
|
||||
#sanity check time
|
||||
@assert length(operator_array) == N_constellations "Mismatch in predetermined number of constellations and the number of operators initialized"
|
||||
|
||||
# Setup Planner
|
||||
pl = PlannerLoss(
|
||||
0.95
|
||||
,operator_array
|
||||
,planners_policy
|
||||
,params(planners_policy)
|
||||
,planners_value
|
||||
,params(planners_value)
|
||||
,basic_model
|
||||
)
|
||||
|
||||
# Export Planner
|
||||
@ -0,0 +1,54 @@
|
||||
using Test,Flux
|
||||
|
||||
include("../src/Orbits.jl")
|
||||
using .Orbits
|
||||
|
||||
|
||||
|
||||
#=
|
||||
Structure:
|
||||
|
||||
This is broken into three parts
|
||||
- The test_interfaces module contains various tools used in testing
|
||||
- The test_routines includes functions that setup, run, and teardown tests
|
||||
- Everything else is a set of tests using the standard testing tools in Julia
|
||||
=#
|
||||
@testset "Overall" verbose=true begin
|
||||
@testset "TupleDuplicator" verbose=true begin
|
||||
#Check if tuple duplicator duplicates something
|
||||
td2 = Orbits.TupleDuplicator(2)
|
||||
@test typeof(td2) <: Orbits.TupleDuplicator
|
||||
|
||||
@test td2(([1,2],[3])) == (([1,2],[3]),([1,2],[3]))
|
||||
|
||||
st = State([1.0,2],[3])
|
||||
@test td2((st.stocks,st.debris)) == (([1.0,2],[3]),([1.0,2],[3]))
|
||||
|
||||
@test td2(state_to_tuple(st)) == (([1.0,2],[3]),([1.0,2],[3]))
|
||||
|
||||
@test td2(st) == ((st.stocks,st.debris),(st.stocks,st.debris))
|
||||
end
|
||||
|
||||
@testset "BranchGenerator" verbose=true begin
|
||||
st = State([1.0,2],[3])
|
||||
tp = state_to_tuple(st)
|
||||
bg = BranchGenerator(2)
|
||||
|
||||
branch = Flux.Parallel(vcat, Dense(2,1),Dense(1,1))
|
||||
|
||||
branched = bg(branch,vcat)
|
||||
|
||||
#type tests
|
||||
@test typeof(branch(tp)) <: Array{Float32}
|
||||
|
||||
@test_broken typeof(branched[2](tp)) <: Array{Float32}
|
||||
#ISSUE: what am I really looking for here?
|
||||
|
||||
#Check behaviors of the
|
||||
@test branched[1](st) == state_to_tuple(st) #Evaluation is of the wrong approach
|
||||
|
||||
|
||||
|
||||
end #branch generator
|
||||
|
||||
end #overall testset
|
||||
@ -0,0 +1,62 @@
|
||||
using Test, Flux, LinearAlgebra
|
||||
|
||||
include("../src/Orbits.jl")
|
||||
using .Orbits
|
||||
|
||||
#=
|
||||
The purpose of this document is to organize tests of the state structs and state transition functions
|
||||
=#
|
||||
|
||||
@testset "States and Physical models testing" verbose=true begin
|
||||
n_const = 2
|
||||
n_debr = 3
|
||||
n_data = 5
|
||||
|
||||
#built structs
|
||||
u = UniformDataConstructor(n_data,0,5,2,3)
|
||||
s = u(n_const,n_debr)
|
||||
b = BasicPhysics(
|
||||
0.05
|
||||
,0.02*LinearAlgebra.ones(n_const,n_const)
|
||||
,0.1
|
||||
,0.002
|
||||
,0.002
|
||||
,0.2
|
||||
)
|
||||
|
||||
a2 = ones(n_const,n_data)
|
||||
|
||||
#test that dimensions match etc
|
||||
@test size(b.satellite_collision_rates)[1] == size(s.stocks)[1]
|
||||
@test size(b.satellite_collision_rates)[2] == size(s.stocks)[1]
|
||||
@test n_data == size(s.stocks)[2]
|
||||
@test n_data == size(s.debris)[2]
|
||||
@test size(s.stocks) == size(a2)
|
||||
|
||||
@testset "DataConstructor and states" begin
|
||||
@test u.N == 5
|
||||
|
||||
@test length(s.debris) != 3
|
||||
@test length(s.stocks) != 2
|
||||
|
||||
@test length(s.stocks) == 10
|
||||
@test length(s.debris) == 15
|
||||
|
||||
@test size(s.stocks) == (2,5)
|
||||
@test size(s.debris) == (3,5)
|
||||
end
|
||||
|
||||
@testset "BasicPhysics" begin
|
||||
@testset "Survival Functions" verbose = true begin
|
||||
@test survival_rates_1(s,b) <: AbstractArray
|
||||
end
|
||||
|
||||
@testset "Transitions" begin
|
||||
@test true
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
end #States and physcial models testing
|
||||
@ -0,0 +1,8 @@
|
||||
{
|
||||
"folders": [
|
||||
{
|
||||
"path": ".."
|
||||
}
|
||||
],
|
||||
"settings": {}
|
||||
}
|
||||
@ -0,0 +1,327 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "0b5021da-575c-4db3-9e01-dc043a7c64b3",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"using DiffEqFlux,Flux,Zygote, LinearAlgebra"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "32ca6032-9d48-4bb2-b16e-4a66473464cd",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"2"
|
||||
]
|
||||
},
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"const N_constellations = 1\n",
|
||||
"const N_debris = 1\n",
|
||||
"const N_states= N_constellations + N_debris"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"id": "77213ba3-1645-45b2-903f-b7f2817cbb47",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"#setup physical model\n",
|
||||
"struct BasicModel\n",
|
||||
" #rate at which debris hits satellites\n",
|
||||
" debris_collision_rate\n",
|
||||
" #rate at which satellites of different constellations collide\n",
|
||||
" satellite_collision_rates\n",
|
||||
" #rate at which debris exits orbits\n",
|
||||
" decay_rate\n",
|
||||
" #rate at which satellites\n",
|
||||
" autocatalysis_rate\n",
|
||||
" #ratio at which a collision between satellites produced debris\n",
|
||||
" satellite_collision_debris_ratio\n",
|
||||
" #Ratio at which launches produce debris\n",
|
||||
" launch_debris_ratio\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"#Getting loss parameters together.\n",
|
||||
"loss_param = 2e-3;\n",
|
||||
"loss_weights = loss_param*(ones(N_constellations,N_constellations) - I);\n",
|
||||
"\n",
|
||||
"#orbital decay rate\n",
|
||||
"decay_param = 0.01;\n",
|
||||
"\n",
|
||||
"#debris generation parameters\n",
|
||||
"autocatalysis_param = 0.001;\n",
|
||||
"satellite_loss_debris_rate = 5.0;\n",
|
||||
"launch_debris_rate = 0.05;\n",
|
||||
"\n",
|
||||
"#Todo, wrap physical model as a struct with the parameters\n",
|
||||
"bm = BasicModel(\n",
|
||||
" loss_param\n",
|
||||
" ,loss_weights\n",
|
||||
" ,decay_param\n",
|
||||
" ,autocatalysis_param\n",
|
||||
" ,satellite_loss_debris_rate\n",
|
||||
" ,launch_debris_rate\n",
|
||||
");\n",
|
||||
"\n",
|
||||
"#implement tranistion function\n",
|
||||
"#percentage survival function\n",
|
||||
"function survival(stocks,debris,physical_model) \n",
|
||||
" exp.(-physical_model.satellite_collision_rates*stocks .- (physical_model.debris_collision_rate*debris));\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"#stock update rules\n",
|
||||
"function G(stocks,debris,launches, physical_model)\n",
|
||||
" return diagm(survival(stocks,debris,physical_model) .- physical_model.decay_rate)*stocks + launches\n",
|
||||
"end;\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"#debris evolution \n",
|
||||
"function H(stocks,debris,launches,physical_model)\n",
|
||||
" #get changes in debris from natural dynamics\n",
|
||||
" natural_debris_dynamics = (1-physical_model.decay_rate+physical_model.autocatalysis_rate) * debris \n",
|
||||
" \n",
|
||||
" #get changes in debris from satellite loss\n",
|
||||
" satellite_loss_debris = physical_model.satellite_collision_debris_ratio * (1 .- survival(stocks,debris,physical_model))'*stocks \n",
|
||||
" \n",
|
||||
" #get changes in debris from launches\n",
|
||||
" launch_debris = physical_model.launch_debris_ratio*sum(launches)\n",
|
||||
" \n",
|
||||
" #return total debris level\n",
|
||||
" return natural_debris_dynamics + satellite_loss_debris + launch_debris\n",
|
||||
"end;\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"#implement reward function\n",
|
||||
"const payoff = 3*I - 0.02*ones(N_constellations,N_constellations)\n",
|
||||
"\n",
|
||||
"#Define the market profit function\n",
|
||||
"F(stocks,debris,launches) = payoff*stocks + 3.0*launches .+ (debris*-0.2)\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 18,
|
||||
"id": "998a1ce8-a6ba-427d-a5d1-fece358146da",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Launch function\n",
|
||||
"launches = Chain(\n",
|
||||
" Parallel(vcat\n",
|
||||
" #parallel joins together stocks and debris, along with intermediate interpretation\n",
|
||||
" ,Chain(Dense(N_constellations, N_states*2,relu)\n",
|
||||
" ,Dense(N_states*2, N_states*2,relu)\n",
|
||||
" )\n",
|
||||
" ,Chain(Dense(N_debris, N_states,relu)\n",
|
||||
" ,Dense(N_states, N_states,relu)\n",
|
||||
" )\n",
|
||||
" #chain gets applied to parallel\n",
|
||||
" ,Dense(N_states*3,128,relu)\n",
|
||||
" #,Dense(128,128,relu)\n",
|
||||
" ,Dense(128,N_constellations,relu)\n",
|
||||
" )\n",
|
||||
");\n",
|
||||
"\n",
|
||||
"#Value functions\n",
|
||||
"∂value = Chain(\n",
|
||||
" Parallel(vcat\n",
|
||||
" #parallel joins together stocks and debris, along with intermediate interpretation\n",
|
||||
" ,Chain(Dense(N_constellations, N_states*2,relu)\n",
|
||||
" ,Dense(N_states*2, N_states*2,relu)\n",
|
||||
" )\n",
|
||||
" ,Chain(Dense(N_debris, N_states,relu)\n",
|
||||
" ,Dense(N_states, N_states,relu)\n",
|
||||
" )\n",
|
||||
" #chain gets applied to parallel\n",
|
||||
" ,Dense(N_states*3,128,relu)\n",
|
||||
" #,Dense(128,128,relu)\n",
|
||||
" ,Dense(128,N_states,relu)\n",
|
||||
" )\n",
|
||||
");"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "b4409af2-7f41-45bc-b7eb-4bda019e4092",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"1-element Vector{Float64}:\n",
|
||||
" 0.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Extract parameter sets\n",
|
||||
"\n",
|
||||
"#= initialize Algorithm Parameters\n",
|
||||
"Chose these randomly\n",
|
||||
"=#\n",
|
||||
"λʷ = 0.5\n",
|
||||
"αʷ = 5.0\n",
|
||||
"λᶿ = 0.5\n",
|
||||
"αᶿ = 5.0\n",
|
||||
"αʳ = 10\n",
|
||||
"\n",
|
||||
"# initialitze averaging returns\n",
|
||||
"r = zeros(N_constellations)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "0529c209-55c0-49c7-815b-47578b029593",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"1-element Vector{Int64}:\n",
|
||||
" 3"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# initial states\n",
|
||||
"S₀ = rand(1:5,N_constellations)\n",
|
||||
"D₀ = rand(1:3, N_debris)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"id": "ae7d4152-77b0-42ff-92f6-9d5d83d6a39d",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Params([Float32[-0.110574484; 1.0583764; 0.039519094; 0.2908444], Float32[0.0, 0.0, 0.0, 0.0], Float32[0.4765299 0.5994208 -0.43710196 0.2269359; 0.5550531 0.5423604 -0.796175 0.76214457; 0.59269524 0.7436546 0.02525105 0.85908467; 0.3774994 -0.111040816 0.84196734 -0.18133782], Float32[0.0, 0.0, 0.0, 0.0], Float32[-1.2003294; -1.24031], Float32[0.0, 0.0], Float32[-0.004074011 -0.84631246; -0.5459394 1.1513239], Float32[0.0, 0.0], Float32[-0.19545768 -0.20670874 … 0.06923863 -0.09825141; 0.097166725 0.06564395 … -0.1928437 0.19962357; … ; 0.025075339 -0.06016964 … 0.0838129 -0.11523932; 0.20085223 0.16679004 … 0.016495213 -0.1548977], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[-0.21479565 0.0090183215 … -0.2022802 -0.19925424], Float32[0.0]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"launch_params = Flux.params(launches)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"id": "232c0a44-be74-4431-a86e-dbc71e83c17a",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"loss (generic function with 1 method)"
|
||||
]
|
||||
},
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"function loss(stocks,debris)\n",
|
||||
" sum(launches((stocks,debris)))\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"id": "e1e1cdef-b164-43b6-a80e-b8665bdf9b14",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Grads(...)"
|
||||
]
|
||||
},
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g = Flux.gradient(() -> loss(S₀,D₀), launch_params)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"id": "35d1763b-4650-4916-957d-fbb436280e1f",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Params([Float32[-0.110574484; 1.0583764; 0.039519094; 0.2908444], Float32[0.0, 0.0, 0.0, 0.0], Float32[0.4765299 0.5994208 -0.43710196 0.2269359; 0.5550531 0.5423604 -0.796175 0.76214457; 0.59269524 0.7436546 0.02525105 0.85908467; 0.3774994 -0.111040816 0.84196734 -0.18133782], Float32[0.0, 0.0, 0.0, 0.0], Float32[-1.2003294; -1.24031], Float32[0.0, 0.0], Float32[-0.004074011 -0.84631246; -0.5459394 1.1513239], Float32[0.0, 0.0], Float32[-0.19545768 -0.20670874 … 0.06923863 -0.09825141; 0.097166725 0.06564395 … -0.1928437 0.19962357; … ; 0.025075339 -0.06016964 … 0.0838129 -0.11523932; 0.20085223 0.16679004 … 0.016495213 -0.1548977], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[-0.21479565 0.0090183215 … -0.2022802 -0.19925424], Float32[0.0]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"launch_params"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "eaad2871-54ed-4674-8405-d4ebb950851d",
|
||||
"metadata": {},
|
||||
"outputs": [],
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||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.6.2",
|
||||
"language": "julia",
|
||||
"name": "julia-1.6"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.6.2"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
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Reference in New Issue