Orbits/Code

COMPUTATIONAL TODO

Completed steps

• implement 'launch function as a function' portion
• substitute the transition functions into the optimality conditions.

Next steps

• create the iterated optimality conditions
  • attach iterated state variables to iterated transitons
  • use these state variables to calculate the optimality condition values
• use these optimality conditions to create a loss function
  • Thoughts on converting my connect_transitions_to_otimality_conditions work to this. I need to import torch into that section, and build a loss function.
  • The basics of this model
  • Use just a basic MSELoss wrapped so that it calculates
• add boundary conditions to loss function
• get a basic gradient descent/optimization of launch function working.
• add satellite deorbit to model.
• turn this into a framework in a module, not just a single notebook (long term goal)

CONCERNS

So I need to think about how to handle the launch functions. Currently, my launch function takes in the stocks and debris levels and returns a launch decision for each constellation. This is nice because it keeps them together, but it may require some thoughtful NeuralNetwork design later. The issue is that I need to set up a way to integrate multiple firms at the same time. This may be possible through how I set up the profit funcitons.

Also, I think I need to write out some

Scratch work

Writing out the functional forms that need to exist and the inheritance

• Euler equation
  • Optimality Conditions
  • Transition functions
• Loss function
  • Bounds
  • Euler equations
• Neural net launch function

Launch & Retire (a neural network) NN(states) -> launch & deorbit decisions

Euler Equations EE(NN, states) -> vector of numbers Consists of Iterated_Optimality(Iterated_Value_Derivatives(NN), Iterated_States(NN))

Loss Function L(EE, Bounds, NN, States) -> positive number