changed gitignore and added the module I'm hoping to build.

.gitignore

@@ -4,11 +4,17 @@
 CurrentWriting/sections/[0-9][0-9]*.pdf
 CurrentWriting/Main.pdf
 
+#Ignore .bson files
+*.bson
+
+
+
 ### SPECIFICALLY INCLUDE
 #Preambles
 !CurrentWriting/assets/preambles/*
 
 
+
 ########### GENERIC STUFF BELOW ###########
 
 ## Core latex/pdflatex auxiliary files:

julia_code/Module/Manifest.toml

@@ -0,0 +1,523 @@
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+[[Statistics]]
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+
+[[StatsAPI]]
+git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
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+
+[[StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
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+
+[[Tar]]
+deps = ["ArgTools", "SHA"]
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+
+[[Test]]
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+
+[[TimerOutputs]]
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+
+[[TranscodingStreams]]
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+
+[[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"
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+
+[[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"
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+
+[[ZygoteRules]]
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+[[p7zip_jll]]
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julia_code/Module/Project.toml

@@ -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"

julia_code/Module/README.md

@@ -0,0 +1 @@
+Description goes here

julia_code/Module/notebooks/splitme.jl

@@ -0,0 +1,846 @@
+### A Pluto.jl notebook ###
+# v0.17.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ b194c2fc-340b-480e-b1ec-53db2fe4e7ec
+module PhysicsModule
+	
+	#Add exports here
+	
+	
+	using Flux, LinearAlgebra
+	using Zygote #included for saving and loading models
+	
+	#==#
+	struct State
+		stocks::Array{Float32}
+		debris::Array{Float32}
+	end
+	
+	
+	### Physics
+	
+	
+	abstract type PhysicalModel end
+		
+	struct BasicModel <: PhysicalModel
+		#rate at which debris hits satellites
+		debris_collision_rate::Real
+		#rate at which satellites of different constellations collide
+		satellite_collision_rates::Matrix{Float64}
+		#rate at which debris exits orbits
+		decay_rate::Real
+		#rate at which satellites
+		autocatalysis_rate::Real
+		#ratio at which a collision between satellites produced debris
+		satellite_collision_debris_ratio::Real
+		#Ratio at which launches produce debris
+		launch_debris_ratio::Real
+	end
+	function state_transition(
+		physics::BasicModel 
+		,state::State 
+		,launches::Vector{Float32}
+		)
+		#=
+		Physical Transitions
+		=#
+		survival_rate = survival(state,physics)
+	
+		# Debris
+	
+		# get changes in debris from natural dynamics
+		natural_debris_dynamics = (1 - physics.decay_rate + physics.autocatalysis_rate) * state.debris 
+		
+		# get changes in debris from satellite loss
+		satellite_loss_debris = physics.satellite_collision_debris_ratio * (1 .- survival_rate)'*state.stocks 
+		
+		# get changes in debris from launches
+		launch_debris = physics.launch_debris_ratio * sum(launches)
+		
+		# total debris level
+		debris′ = natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
+	
+	
+		#stocks
+		stocks′ = (LinearAlgebra.diagm(survival_rate) .- physics.decay_rate)*state.stocks + launches
+	
+	
+		return State(stocks′,debris′)
+	end 
+	
+	
+	function survival(
+			state::State
+			,physical_model::BasicModel
+		)	
+	    return exp.(
+			-(physical_model.satellite_collision_rates .+ physical_model.decay_rate) * state.stocks 
+			.- (physical_model.debris_collision_rate * state.debris)
+		)
+	end
+end #end physccs
+
+# ╔═╡ 85897da8-bc22-40bd-8ec7-853f86ac4941
+module NNTools
+#= TupleDuplicator
+This is used to create a tuple of size n with deepcopies of any object x
+=#
+
+using Flux,Zygote,BSON
+
+struct TupleDuplicator
+	n::Int
+end
+(f::TupleDuplicator)(x) = tuple([deepcopy(x) for i=1:f.n]...)
+
+#=
+This generates a policy function full of branches with the properly scaled sides
+=#
+struct BranchGenerator
+	n::UInt8 
+	#limit to 2^8 operators
+end
+function (b::BranchGenerator)(branch::Flux.Chain,join_fn::Function) 
+	# used to deepcopy the branches and duplicate the inputs in the returned chain
+	f = TupleDuplicator(b.n)
+	
+	return Flux.Chain(f,Flux.Parallel(join_fn,f(branch)))
+end
+
+## Couple of helpful policy generators, just for help.
+
+function operator_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.tanh)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.tanh)
+			,Flux.Dense(number_params,number_params,Flux.tanh)
+			,Flux.Dense(number_params,1,x -> Flux.relu.(sinh.(x)))
+		)
+
+end
+
+function planner_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,N_constellations,Flux.relu)
+		)
+
+end
+
+function value_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris, after a little bit of preprocessing
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params,Flux.σ)
+				)
+			)
+		    #Apply some transformations to the preprocessed data.
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,1)
+		)
+
+end
+
+end
+
+# ╔═╡ 4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
+using LinearAlgebra, BSON
+
+# ╔═╡ 99aabead-81d0-4f66-994a-bc5485c08af5
+### Economics
+	module EconomicModule
+	abstract type EconomicModel end
+	
+	#basic linear model
+	struct LinearModel <: EconomicModel
+		β::Float32
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+	end
+	function (em::LinearModel)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+		return em.payoff_array*s - em.policy_costs*a
+	end
+	
+	#basic CES model
+	struct CES <: EconomicModel
+		β::Float32
+		r::Float32 #elasticity of subsititution
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+		debris_costs::Array{Float32}
+	end
+	function (em::CES)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+	
+		#issue here with multiplication
+		r1 = em.payoff_array .* (s.^em.r) 
+		r2 = - em.debris_costs .* (d.^em.r) 
+		r3 = - em.policy_costs .* (a.^em.r)
+		return (r1 + r2 + r3) .^ (1/em.r)
+	
+	end
+	
+	#basic CRRA
+	struct CRRA <: EconomicModel
+		β::Float32
+		σ::Float32 #elasticity of subsititution
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+		debris_costs::Array{Float32}
+	end
+	function (em::CRRA)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+		#issue here with multiplication
+		core = (em.payoff_array*s - em.debris_costs*d - em.policy_costs).^(1 - em.σ)
+	
+		return (core-1)/(1-em.σ)
+	end
+	
+end #end module
+
+# ╔═╡ 3be917ed-7107-46a3-bd8e-969e0e8e0fea
+md"""
+# testing
+
+Define the basic dimensions of the model
+ - Number of Constellations: $(const N_constellations = 4)
+ - Number of Debris Trackers: $(const N_debris = 1)
+ - Number of Overall States: $(const N_states = N_constellations + N_debris)
+"""
+
+# ╔═╡ f4d11666-dd44-4340-8fe7-b5cf735dea67
+md"""
+## Physics
+"""
+
+# ╔═╡ 30622c11-32f3-4b68-b391-e526c3b09570
+begin #Setup for State tests
+	st = OD.State([1,2,3,4],[3])
+	launches = zeros(Float32,4)
+
+	loss_param = 2e-3;
+	loss_weights = loss_param*(ones(N_constellations,N_constellations) - LinearAlgebra.I);
+	
+
+	#Todo, wrap physical model as a struct with the parameters
+	bm = OD.BasicModel(
+		loss_param
+		,loss_weights
+		,0.01
+		,0.001
+		,5.0
+		,0.05
+	)
+end
+
+# ╔═╡ 5497cf84-0fc1-4d47-8a1d-58f862000828
+OD.state_transition(bm,st,launches)
+
+# ╔═╡ 7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
+md"""
+## Neural Networks
+"""
+
+# ╔═╡ f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
+md"""
+## Operator Models
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[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"
+
+[compat]
+BSON = "~0.3.4"
+Flux = "~0.12.8"
+Zygote = "~0.6.30"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
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+
+[[ArgTools]]
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+
+[[ArrayInterface]]
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+
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+
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+
+[[BSON]]
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+[[LLVM]]
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+[[LibCURL]]
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+
+[[LibCURL_jll]]
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+
+[[LibGit2]]
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+
+[[LibSSH2_jll]]
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+
+[[Libdl]]
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+[[LinearAlgebra]]
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+[[LogExpFunctions]]
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+[[Logging]]
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+[[MacroTools]]
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+
+[[Markdown]]
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+
+[[MbedTLS_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
+
+[[Media]]
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+uuid = "e89f7d12-3494-54d1-8411-f7d8b9ae1f27"
+version = "0.5.0"
+
+[[Missings]]
+deps = ["DataAPI"]
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+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"
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+
+[[NNlibCUDA]]
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+git-tree-sha1 = "38358632d9c277f7bf8d202c127f601e8467aa4d"
+uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
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+
+[[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"
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+
+[[RandomNumbers]]
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+
+[[RealDot]]
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+uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
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+
+[[Reexport]]
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+
+[[Requires]]
+deps = ["UUIDs"]
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+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"]
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+[[SparseArrays]]
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+
+[[SpecialFunctions]]
+deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
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+[[Static]]
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+[[StaticArrays]]
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+
+[[Statistics]]
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+
+[[StatsAPI]]
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+[[StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
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+[[TOML]]
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+
+[[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"
+"""
+
+# ╔═╡ Cell order:
+# ╠═b194c2fc-340b-480e-b1ec-53db2fe4e7ec
+# ╠═99aabead-81d0-4f66-994a-bc5485c08af5
+# ╠═85897da8-bc22-40bd-8ec7-853f86ac4941
+# ╟─3be917ed-7107-46a3-bd8e-969e0e8e0fea
+# ╠═f4d11666-dd44-4340-8fe7-b5cf735dea67
+# ╠═4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
+# ╠═30622c11-32f3-4b68-b391-e526c3b09570
+# ╠═5497cf84-0fc1-4d47-8a1d-58f862000828
+# ╠═7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
+# ╠═f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002

julia_code/Module/splitme.jl

@@ -0,0 +1,962 @@
+### A Pluto.jl notebook ###
+# v0.17.1
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ b194c2fc-340b-480e-b1ec-53db2fe4e7ec
+module PhysicsModule
+	
+	#Add exports here
+	
+	
+	using Flux, LinearAlgebra
+	using Zygote #included for saving and loading models
+	
+	#==#
+	struct State
+		stocks::Array{Float32}
+		debris::Array{Float32}
+	end
+	
+	
+	### Physics
+	
+	
+	abstract type PhysicalModel end
+		
+	struct BasicModel <: PhysicalModel
+		#rate at which debris hits satellites
+		debris_collision_rate::Real
+		#rate at which satellites of different constellations collide
+		satellite_collision_rates::Matrix{Float64}
+		#rate at which debris exits orbits
+		decay_rate::Real
+		#rate at which satellites
+		autocatalysis_rate::Real
+		#ratio at which a collision between satellites produced debris
+		satellite_collision_debris_ratio::Real
+		#Ratio at which launches produce debris
+		launch_debris_ratio::Real
+	end
+	function state_transition(
+		physics::BasicModel 
+		,state::State 
+		,launches::Vector{Float32}
+		)
+		#=
+		Physical Transitions
+		=#
+		survival_rate = survival(state,physics)
+	
+		# Debris
+	
+		# get changes in debris from natural dynamics
+		natural_debris_dynamics = (1 - physics.decay_rate + physics.autocatalysis_rate) * state.debris 
+		
+		# get changes in debris from satellite loss
+		satellite_loss_debris = physics.satellite_collision_debris_ratio * (1 .- survival_rate)'*state.stocks 
+		
+		# get changes in debris from launches
+		launch_debris = physics.launch_debris_ratio * sum(launches)
+		
+		# total debris level
+		debris′ = natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
+	
+	
+		#stocks
+		stocks′ = (LinearAlgebra.diagm(survival_rate) .- physics.decay_rate)*state.stocks + launches
+	
+	
+		return State(stocks′,debris′)
+	end 
+	
+	
+	function survival(
+			state::State
+			,physical_model::BasicModel
+		)	
+	    return exp.(
+			-(physical_model.satellite_collision_rates .+ physical_model.decay_rate) * state.stocks 
+			.- (physical_model.debris_collision_rate * state.debris)
+		)
+	end
+end #end physccs
+
+# ╔═╡ 4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
+using LinearAlgebra, BSON
+
+# ╔═╡ 85897da8-bc22-40bd-8ec7-853f86ac4941
+module NNTools
+#= TupleDuplicator
+This is used to create a tuple of size n with deepcopies of any object x
+=#
+
+using Flux,Zygote,BSON
+
+struct TupleDuplicator
+	n::Int
+end
+(f::TupleDuplicator)(x) = tuple([deepcopy(x) for i=1:f.n]...)
+
+#=
+This generates a policy function full of branches with the properly scaled sides
+=#
+struct BranchGenerator
+	n::UInt8 
+	#limit to 2^8 operators
+end
+function (b::BranchGenerator)(branch::Flux.Chain,join_fn::Function) 
+	# used to deepcopy the branches and duplicate the inputs in the returned chain
+	f = TupleDuplicator(b.n)
+	
+	return Flux.Chain(f,Flux.Parallel(join_fn,f(branch)))
+end
+
+## Couple of helpful policy generators, just for help.
+
+function operator_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.tanh)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.tanh)
+			,Flux.Dense(number_params,number_params,Flux.tanh)
+			,Flux.Dense(number_params,1,x -> Flux.relu.(sinh.(x)))
+		)
+
+end
+
+function planner_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,N_constellations,Flux.relu)
+		)
+
+end
+
+function value_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris, after a little bit of preprocessing
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params,Flux.σ)
+				)
+			)
+		    #Apply some transformations to the preprocessed data.
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,1)
+		)
+
+end
+
+end
+
+# ╔═╡ 3be917ed-7107-46a3-bd8e-969e0e8e0fea
+md"""
+# testing
+
+Define the basic dimensions of the model
+ - Number of Constellations: $(const N_constellations = 4)
+ - Number of Debris Trackers: $(const N_debris = 1)
+ - Number of Overall States: $(const N_states = N_constellations + N_debris)
+"""
+
+# ╔═╡ f4d11666-dd44-4340-8fe7-b5cf735dea67
+md"""
+## Physics
+"""
+
+# ╔═╡ 30622c11-32f3-4b68-b391-e526c3b09570
+begin #Setup for State tests
+	st = PhysicsModule.State([1,2,3,4],[3])
+	launches = zeros(Float32,4)
+
+	loss_param = 2e-3;
+	loss_weights = loss_param*(ones(N_constellations,N_constellations) - LinearAlgebra.I);
+	
+
+	#Todo, wrap physical model as a struct with the parameters
+	bm = PhysicsModule.BasicModel(
+		loss_param
+		,loss_weights
+		,0.01
+		,0.001
+		,5.0
+		,0.05
+	)
+end
+
+# ╔═╡ 5497cf84-0fc1-4d47-8a1d-58f862000828
+PhysicsModule.state_transition(bm,st,launches)
+
+# ╔═╡ 7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
+md"""
+## Neural Networks
+"""
+
+# ╔═╡ 2879d65a-4a2e-4486-ac26-a0490a80f23e
+NNTools.value_function_generator()
+
+# ╔═╡ f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
+md"""
+## Operator Models
+"""
+
+# ╔═╡ 99aabead-81d0-4f66-994a-bc5485c08af5
+### Economics
+module BenefitFunctions
+	abstract type EconomicModel end
+	
+	#basic linear model
+	struct LinearModel <: EconomicModel
+		β::Float32
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+	end
+	function (em::LinearModel)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+		return em.payoff_array*s - em.policy_costs*a
+	end
+	
+	#basic CES model
+	struct CES <: EconomicModel
+		β::Float32
+		r::Float32 #elasticity of subsititution
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+		debris_costs::Array{Float32}
+	end
+	function (em::CES)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+	
+		#issue here with multiplication
+		r1 = em.payoff_array .* (s.^em.r) 
+		r2 = - em.debris_costs .* (d.^em.r) 
+		r3 = - em.policy_costs .* (a.^em.r)
+		return (r1 + r2 + r3) .^ (1/em.r)
+	
+	end
+	
+	#basic CRRA
+	struct CRRA <: EconomicModel
+		β::Float32
+		σ::Float32 #elasticity of subsititution
+		payoff_array::Array{Float32}
+		policy_costs::Array{Float32}
+		debris_costs::Array{Float32}
+	end
+	function (em::CRRA)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,a::Vector{Float32}
+		)
+		#issue here with multiplication
+		core = (em.payoff_array*s - em.debris_costs*d - em.policy_costs).^(1 - em.σ)
+	
+		return (core-1)/(1-em.σ)
+	end
+	
+end #end module
+
+# ╔═╡ 473c1c21-c3b8-4ca8-8e76-cc42b3ea0da4
+begin
+	#=
+	This struct organizes information about a given constellation operator
+	Used to provide an interable loss function for training
+
+	=#
+	struct ConstellationOperatorLoss
+		#econ model describing operator
+		econ_model::EconomicModel
+		#Operator's value and policy functions, as well as which parameters the operator can train.
+		operator_value_fn::Flux.Chain
+		collected_policies::Flux.Chain #this is held by all operators
+		operator_policy_params::Flux.Params
+		#Transition functions
+		debris_transition::BasicDebrisEvolution
+		stocks_transition::BasicStockEvolution
+	end
+	# overriding function to calculate operator loss
+	function (operator::ConstellationOperatorLoss)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+	)
+		
+
+		#get actions
+		a = operator.collected_policies((s,d))
+	
+		#get updated stocks and debris
+		s′ = operator.stocks_transition(s ,d ,a)
+		d′ = operator.debris_transition(s ,d ,a)
+	
+		
+		bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+		
+		maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+	
+		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+	end
+	
+	function (operator::ConstellationOperatorLoss)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+		,policy::Flux.Chain #allow for another policy to be subsituted
+	)
+		
+
+		#get actions
+		a = policy((s,d))
+	
+		#get updated stocks and debris
+		s′ = operator.stocks_transition(s ,d ,a)
+		d′ = operator.debris_transition(s ,d ,a)
+	
+		
+		bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+		
+		maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+	
+		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+	end
+end
+
+# ╔═╡ c5d4b5af-ec04-4941-b84f-c70e9665810b
+begin
+	
+	#do the same thing with the planner's problem
+	struct PlannerLoss
+		#=
+		Ideally, with just a well formed PlannerLoss and the training functions below, we should be able to train the approximation.
+
+		There is an issue with appropriately training the value functions.
+		In this case, it is not happening...
+		=#
+		β::Float32
+		
+		operators::Array{ConstellationOperatorLoss}
+		
+		policy::Flux.Chain
+		policy_params::Flux.Params
+		value::Flux.Chain
+		value_params::Flux.Params
+		
+		debris_transition::BasicDebrisEvolution
+		stocks_transition::BasicStockEvolution
+	end
+	function (planner::PlannerLoss)(
+		s::Vector{Float32}
+		,d::Vector{Float32}
+	) 
+		a = planner.policy((s ,d))
+		#get updated stocks and debris
+		s′ = planner.stocks_transition(s ,d ,a)
+		d′ = planner.debris_transition(s ,d ,a)
+		
+		
+		
+			#calculate the total benefit from each of the models
+		benefit = sum([ co.econ_model(s ,d ,a) for co in planner.operators])
+			#issue here with mutating. Maybe generators/list comprehensions?
+		
+		
+		bellman_residuals = planner.value((s,d)) - benefit - planner.β .* planner.value((s′,d′))
+
+		maximization_condition = - benefit - planner.β .* planner.value((s′,d′))
+		
+		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+	end
+end
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[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"
+
+[compat]
+BSON = "~0.3.4"
+Flux = "~0.12.8"
+Zygote = "~0.6.30"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
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+[[Test]]
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+[[ZipFile]]
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+[[Zlib_jll]]
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+
+[[Zygote]]
+deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "2c30f2df0ba43c17e88c8b55b5b22c401f7cde4e"
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+
+[[ZygoteRules]]
+deps = ["MacroTools"]
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+[[nghttp2_jll]]
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+
+[[p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+"""
+
+# ╔═╡ Cell order:
+# ╟─b194c2fc-340b-480e-b1ec-53db2fe4e7ec
+# ╟─3be917ed-7107-46a3-bd8e-969e0e8e0fea
+# ╠═f4d11666-dd44-4340-8fe7-b5cf735dea67
+# ╠═4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
+# ╠═30622c11-32f3-4b68-b391-e526c3b09570
+# ╠═5497cf84-0fc1-4d47-8a1d-58f862000828
+# ╠═7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
+# ╟─85897da8-bc22-40bd-8ec7-853f86ac4941
+# ╠═2879d65a-4a2e-4486-ac26-a0490a80f23e
+# ╠═f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
+# ╟─99aabead-81d0-4f66-994a-bc5485c08af5
+# ╠═473c1c21-c3b8-4ca8-8e76-cc42b3ea0da4
+# ╠═c5d4b5af-ec04-4941-b84f-c70e9665810b
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002

julia_code/Module/src/Orbits.jl

@@ -0,0 +1,119 @@
+module Orbits
+
+using Flux,LinearAlgebra,Zygote
+
+include("physical_model.jl")
+using .PhysicsModule
+
+include("benefit_functions.jl")
+using .BenefitFunctions
+
+include("flux_helpers.jl")
+using .NNTools
+
+# Exports
+
+
+
+# Code
+
+abstract type GeneralizedLoss end
+
+#=
+This struct organizes information about a given constellation operator
+Used to provide an interable loss function for training
+=#
+struct OperatorLoss <: GeneralizedLoss
+        #econ model describing operator
+        econ_model::EconomicModel
+        #Operator's value and policy functions, as well as which parameters the operator can train.
+        operator_value_fn::Flux.Chain
+        collected_policies::Flux.Chain #this is held by all operators
+        operator_policy_params::Flux.Params
+        physics::PhysicalModel
+end
+# overriding function to calculate operator loss
+function (operator::OperatorLoss)(
+        s::Vector{Float32}
+        ,d::Vector{Float32}
+)
+
+
+        #get actions
+        a = operator.collected_policies((s,d))
+
+        #get updated stocks and debris
+        s′ = operator.stocks_transition(s ,d ,a)
+        d′ = operator.debris_transition(s ,d ,a)
+
+
+        bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+
+        maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+
+        return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+end # struct
+function (operator::OperatorLoss)(
+        state::State
+        ,policy::Flux.Chain #allow for another policy to be subsituted
+)
+
+
+        #get actions
+        a = policy((s,d))
+
+        #get updated stocks and debris
+        s′ = operator.stocks_transition(s ,d ,a)
+        d′ = operator.debris_transition(s ,d ,a)
+
+
+        bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+
+        maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
+
+        return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+end #function
+
+#=
+Describe the Planners loss function
+=#
+struct PlannerLoss <: GeneralizedLoss
+        #=
+        Ideally, with just a well formed PlannerLoss and the training functions below, we should be able to train the approximation.
+
+        There is an issue with appropriately training the value functions.
+        In this case, it is not happening...
+        =#
+        β::Float32
+
+        operators::Array{GeneralizedLoss}
+
+        policy::Flux.Chain
+        policy_params::Flux.Params
+        value::Flux.Chain
+        value_params::Flux.Params
+
+        physical_model::PhysicalModel
+end
+function (planner::PlannerLoss)(
+        state::State
+)
+        a = planner.policy((s ,d))
+        #get updated stocks and debris
+        state′ = state_transition(s ,d ,a)
+
+
+
+                #calculate the total benefit from each of the models
+        benefit = sum([ co.econ_model(s ,d ,a) for co in planner.operators])
+                #issue here with mutating. Maybe generators/list comprehensions?
+
+
+        bellman_residuals = planner.value((s,d)) - benefit - planner.β .* planner.value((s′,d′))
+
+        maximization_condition = - benefit - planner.β .* planner.value((s′,d′))
+
+        return Flux.mae(bellman_residuals.^2 ,maximization_condition)
+end
+
+end # end module

julia_code/Module/src/benefit_functions.jl

@@ -0,0 +1,69 @@
+
+module BenefitFunctions
+
+export LinearModel, BenefitFunction
+
+
+import("physical_model.lj")
+using PhysicalModel: State
+
+#=
+Benefit Functions:
+
+These represent the benefits that different operators may recieve
+=#
+abstract type EconomicModel end
+
+#basic linear model
+struct LinearModel <: EconomicModel
+        β::Float32
+        payoff_array::Array{Float32}
+        policy_costs::Array{Float32}
+end
+function (em::LinearModel)(
+        state::State
+        ,a::Vector{Float32}
+        )
+        return em.payoff_array*s - em.policy_costs*a
+end
+
+#basic CES model
+struct CES <: EconomicModel
+        β::Float32
+        r::Float32 #elasticity of subsititution
+        payoff_array::Array{Float32}
+        policy_costs::Array{Float32}
+        debris_costs::Array{Float32}
+end
+function (em::CES)(
+        state::State
+        ,a::Vector{Float32}
+        )
+
+        #issue here with multiplication
+        r1 = em.payoff_array .* (s.^em.r)
+        r2 = - em.debris_costs .* (d.^em.r)
+        r3 = - em.policy_costs .* (a.^em.r)
+        return (r1 + r2 + r3) .^ (1/em.r)
+
+end
+
+#basic CRRA
+struct CRRA <: EconomicModel
+        β::Float32
+        σ::Float32 #elasticity of subsititution
+        payoff_array::Array{Float32}
+        policy_costs::Array{Float32}
+        debris_costs::Array{Float32}
+end
+function (em::CRRA)(
+        state::State
+        ,a::Vector{Float32}
+        )
+        #issue here with multiplication
+        core = (em.payoff_array*s - em.debris_costs*d - em.policy_costs).^(1 - em.σ)
+
+        return (core-1)/(1-em.σ)
+end
+
+end #end module

julia_code/Module/src/flux_helpers.jl

@@ -0,0 +1,99 @@
+module NN Tools
+
+export BranchGenerator, value_function_generator
+
+using Flux, BSON, Zygote
+
+#= TupleDuplicator
+This is used to create a tuple of size n with deepcopies of any object x
+=#
+struct TupleDuplicator
+        n::Int
+end
+(f::TupleDuplicator)(x) = tuple([deepcopy(x) for i=1:f.n]...)
+
+
+
+
+#= BranchGenerator
+This generates a policy function full of branches with the properly scaled sides
+=#
+struct BranchGenerator
+        n::UInt8 
+        #limit to 2^8 operators
+end
+function (b::BranchGenerator)(branch::Flux.Chain,join_fn::Function) 
+        # used to deepcopy the branches and duplicate the inputs in the returned chain
+        f = TupleDuplicator(b.n)
+        
+        return Flux.Chain(f,Flux.Parallel(join_fn,f(branch)))
+        #note that it both uses and runs the tuple duplicator f
+end
+
+
+# Neural Network Generators
+
+function value_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris, after a little bit of preprocessing
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params,Flux.σ)
+				)
+			)
+		    #Apply some transformations to the preprocessed data.
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,1)
+		)
+
+end
+
+function cross_linked_planner_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.σ)
+			,Flux.Dense(number_params,number_params,Flux.σ)
+			,Flux.Dense(number_params,N_constellations,Flux.relu)
+		)
+
+end
+
+function operator_policy_function_generator(number_params=32)
+	return Flux.Chain(
+	    Flux.Parallel(vcat
+		        #parallel joins together stocks and debris
+		        ,Flux.Chain(
+					Flux.Dense(N_constellations, number_params*2,Flux.relu)
+		            ,Flux.Dense(number_params*2, number_params*2,Flux.tanh)
+		        )
+		        ,Flux.Chain(
+					Flux.Dense(N_debris, number_params,Flux.relu)
+		            ,Flux.Dense(number_params, number_params)
+				)
+			)
+		    #Apply some transformations
+			,Flux.Dense(number_params*3,number_params,Flux.tanh)
+			,Flux.Dense(number_params,number_params,Flux.tanh)
+			,Flux.Dense(number_params,1,x -> Flux.relu.(sinh.(x)))
+		)
+
+end
+
+end

julia_code/Module/src/fundamentals.jl

@@ -0,0 +1,15 @@
+module Fundamentals
+	
+#Add exports here
+export State
+
+
+#=
+The state of the world.
+=#
+struct State
+        stocks::Array{Float32}
+        debris::Array{Float32}
+end
+	
+end #end module

julia_code/Module/src/physical_model.jl

@@ -0,0 +1,78 @@
+module PhysicsModule
+
+#Add exports here
+export State, PhysicalModel, BasicModel
+
+
+using Flux, LinearAlgebra
+using Zygote #included for saving and loading models
+
+#==#
+struct State
+        stocks::Array{Float32}
+        debris::Array{Float32}
+end
+
+
+### Physics
+
+
+abstract type PhysicalModel end
+        
+struct BasicModel <: PhysicalModel
+        #rate at which debris hits satellites
+        debris_collision_rate::Real
+        #rate at which satellites of different constellations collide
+        satellite_collision_rates::Matrix{Float64}
+        #rate at which debris exits orbits
+        decay_rate::Real
+        #rate at which satellites
+        autocatalysis_rate::Real
+        #ratio at which a collision between satellites produced debris
+        satellite_collision_debris_ratio::Real
+        #Ratio at which launches produce debris
+        launch_debris_ratio::Real
+end
+function state_transition(
+        physics::BasicModel 
+        ,state::State 
+        ,launches::Vector{Float32}
+        )
+        #=
+        Physical Transitions
+        =#
+        survival_rate = survival(state,physics)
+
+        # Debris
+
+        # get changes in debris from natural dynamics
+        natural_debris_dynamics = (1 - physics.decay_rate + physics.autocatalysis_rate) * state.debris 
+        
+        # get changes in debris from satellite loss
+        satellite_loss_debris = physics.satellite_collision_debris_ratio * (1 .- survival_rate)' * state.stocks 
+        
+        # get changes in debris from launches
+        launch_debris = physics.launch_debris_ratio * sum(launches)
+        
+        # total debris level
+        debris′ = natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
+
+
+        #stocks
+        stocks′ = (LinearAlgebra.diagm(survival_rate) .- physics.decay_rate)*state.stocks + launches
+
+
+        return State(stocks′,debris′)
+end 
+
+
+function survival(
+                state::State
+                ,physical_model::BasicModel
+        )	
+    return exp.(
+                -(physical_model.satellite_collision_rates .+ physical_model.decay_rate) * state.stocks 
+                .- (physical_model.debris_collision_rate * state.debris)
+        )
+end
+end #end module