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### 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"
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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 = """
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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]]
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uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"
[[Pkg]]
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
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[[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]]
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git-tree-sha1 = "043da614cc7e95c703498a491e2c21f58a2b8111"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.5.3"
[[RealDot]]
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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]]
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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"
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[[TranscodingStreams]]
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uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"
[[UUIDs]]
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uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[ZipFile]]
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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]]
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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"
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[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
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[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
"""
# ╔═╡ Cell order:
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# ╠═4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
# ╠═30622c11-32f3-4b68-b391-e526c3b09570
# ╠═5497cf84-0fc1-4d47-8a1d-58f862000828
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# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002