From 3ecc922087e107333a742a6a27f74fcf3f653549 Mon Sep 17 00:00:00 2001 From: youainti Date: Fri, 23 Jul 2021 16:50:54 -0700 Subject: [PATCH] Changes to computation section --- .../sections/07_ComputationalApproach.tex | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/CurrentWriting/sections/07_ComputationalApproach.tex b/CurrentWriting/sections/07_ComputationalApproach.tex index b276d71..0866351 100644 --- a/CurrentWriting/sections/07_ComputationalApproach.tex +++ b/CurrentWriting/sections/07_ComputationalApproach.tex @@ -15,6 +15,10 @@ $0 = f^2(x(\theta),\theta)$, allowing one to find $x(\dot)$ as the solution to a minimization problem. By choosing a neural network as the functional approximation, we are able to +use the fact that a NN with a single hidden layer can be used to approximate +functions arbitrarily well +under certain conditions\footnote{FIND REFERENCE, SEE MALIAR}. +We can also take advantage of the significant computational and practical improvements currently revolutionizing Machine Learning. In particular, we can now use common frameworks, such as python, PyTorch, @@ -22,7 +26,7 @@ and various online accerators (Google Colab) which have been optimized for relatively high performance and straightforward development. -\subsubsection{Computational Plan} +\subsection{Computational Plan} I have decided to use python and the PyTorch Neural Network library for this project. The most difficult step is creating the euler equations. @@ -120,4 +124,17 @@ I am currently working on a plan to guarantee existence of solutions. Some of what I want to do is check numerically crucial values as well as examine the necessary Inada conditions. + +\subsection{Computational Results} +Cases to consider +\begin{itemize} + \item Reproduce Rao Rondina model + \item Reproduce Adilov, perfect competition, cornot-like market. + \item Add military operators to Adilov's model. + This will involve some sort of complementarities. + \item Competitive market where the number of satellites improves quality, i.e. allows + for pricing differences (Orbital Internet and comms). + \item Interacting orbital shells, using a vector of debris. +\end{itemize} + \end{document}