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nmheimnmheim
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fix make file
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‎docs/make.jl‎

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@@ -124,20 +124,20 @@ makedocs(;
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ansicolor=true,
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),
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pages = [
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#"Home" => "index.md",
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#"Installation" => "installation.md",
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#"Projects" => "projects.md",
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#"1: Introduction" => lecture_01,
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#"2: The power of Type System & multiple dispatch" => lecture_02,
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#"3: Design patterns" => lecture_03,
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#"4: Packages development, Unit Tests & CI" => lecture_04,
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#"5: Benchmarking, profiling, and performance gotchas" => lecture_05,
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#"6: Language introspection" => lecture_06,
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#"7: Macros" => lecture_07,
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#"8: Introduction to automatic differentiation" => lecture_08,
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#"9: Manipulating intermediate representation" => lecture_09,
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#"10: Different levels of parallel programming" => lecture_10,
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#"11: Julia for GPU programming" => lecture_11,
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"Home" => "index.md",
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"Installation" => "installation.md",
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"Projects" => "projects.md",
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"1: Introduction" => lecture_01,
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"2: The power of Type System & multiple dispatch" => lecture_02,
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"3: Design patterns" => lecture_03,
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"4: Packages development, Unit Tests & CI" => lecture_04,
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"5: Benchmarking, profiling, and performance gotchas" => lecture_05,
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"6: Language introspection" => lecture_06,
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"7: Macros" => lecture_07,
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"8: Introduction to automatic differentiation" => lecture_08,
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"9: Manipulating intermediate representation" => lecture_09,
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"10: Different levels of parallel programming" => lecture_10,
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"11: Julia for GPU programming" => lecture_11,
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"12: Uncertainty propagation in ODE" => lecture_12,
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"13: Learning ODE from data" => lecture_13,
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#"How to submit homeworks" => "how_to_submit_hw.md",

‎docs/src/lecture_12/lab-ode.jl‎

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struct ODEProblem{F,T<:Tuple{Number,Number},U<:AbstractVector,P<:AbstractVector}
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f::F
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tspan::T
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u0::U
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θ::P
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end
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abstract type ODESolver end
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struct Euler{T} <: ODESolver
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dt::T
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end
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function (solver::Euler)(prob::ODEProblem, u, t)
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f, θ, dt = prob.f, prob.θ, solver.dt
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(u + dt*f(u,θ), t+dt)
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end
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function solve(prob::ODEProblem, solver::ODESolver)
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t = prob.tspan[1]; u = prob.u0
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us = [u]; ts = [t]
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while t < prob.tspan[2]
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(u,t) = solver(prob, u, t)
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push!(us,u)
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push!(ts,t)
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end
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ts, reduce(hcat,us)
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end
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# Define & Solve ODE
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function lotkavolterra(x,θ)
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α, β, γ, δ = θ
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x₁, x₂ = x
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dx₁ = α*x₁ - β*x₁*x₂
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dx₂ = δ*x₁*x₂ - γ*x₂
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[dx₁, dx₂]
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end
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θ = [0.1,0.2,0.3,0.2]
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u0 = [1.0,1.0]
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tspan = (0.,100.)
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prob = ODEProblem(lotkavolterra,tspan,u0,θ)
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‎docs/src/lecture_13/lab.jl‎

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using LinearAlgebra
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using Statistics
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θ = [0.1,GaussNum(0.2,0.1),0.3,0.2]
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u0 = [GaussNum(1.0,0.1),GaussNum(1.0,0.1)]
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tspan = (0.,100.)
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dt = 0.1
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prob = ODEProblem(f,tspan,u0,θ)
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isuncertain(x::GaussNum) = x.σ!=0
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isuncertain(x::Number) = false
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sig(x::GaussNum) = x.σ
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mu(x::GaussNum) = x.μ
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#struct UncertainODEProblem{OP<:ODEProblem,S0<:AbstractMatrix,S<:AbstractMatrix,X<:AbstractMatrix,I,J}
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# prob::OP
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# √Σ::S0
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# Xp::X
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# u_idx::I
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# θ_idx::J
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# function UncertainODEProblem(prob::OP) where OP<:ODEProblem
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# u_idx = findall(isuncertain, prob.u0)
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# θ_idx = findall(isuncertain, prob.θ)
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#
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# uσ = [u.σ for u in prob.u0[u_idx]]
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# θσ = [θ.σ for θ in prob.θ[θ_idx]]
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# √Σ = Diagonal(vcat(uσ,θσ))
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#
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# n = (length(uσ)+length(θσ))*2
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# Qp = sqrt(n) * [I(n) -I(n)]
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# Xp = vcat(prob.u0,prob.θ) .+ √Σ*Qp
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# Σ = √Σ * √Σ'
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#
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# new{OP,typeof(√Σ),typeof(u_idx),typeof(θ_idx)}(prob,√Σ,u_idx,θ_idx)
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# end
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#end
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struct UncertainODEProblem{OP,US,I,J} <: AbstractODEProblem
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prob::OP
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U0::US
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u_idx::I
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θ_idx::J
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function UncertainODEProblem(prob::ODEProblem)
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u_idx = findall(isuncertain, prob.u0)
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θ_idx = findall(isuncertain, prob.θ)
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idx = vcat(u_idx, length(prob.u0) .+ θ_idx)
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n = length(idx)
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Qp = hcat(map(idx) do i
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q = zeros(length(prob.u0)+length(prob.θ))
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q[i] = sqrt(n)
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q
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end, map(idx) do i
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q = zeros(length(prob.u0)+length(prob.θ))
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q[i] = -sqrt(n)
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q
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end)
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Qp = reduce(hcat,Qp)
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Σ_ = Diagonal(vcat(sig.(prob.u0), sig.(prob.θ)))
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μ0 = vcat(mu.(prob.u0),mu.(prob.θ)) .+ Σ_*Qp
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#U0 = μ0 .± diag(Σ_)
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prob = ODEProblem(prob.f, prob.tspan, mu.(prob.u0), mu.(prob.θ))
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new{typeof(prob),typeof(μ0),typeof(u_idx),typeof(θ_idx)}(prob,μ0,u_idx,θ_idx)
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end
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end
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nr_uncertainties(p::UncertainODEProblem) = length(p.u_idx)+length(p.θ_idx)
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struct UncertainODESolver{S<:ODESolver} <: ODESolver
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solver::S
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end
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# function get_xp(p::UncertainODEProblem,i::Int)
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# xp = p.Xp[:,i]
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# u = xp[p.u_idx]
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# θ = p.prob.θ
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# θ[p.θ_idx] .= xp[length(p.u_idx)+1:end]
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# (u,θ)
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# end
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function setmean!(p::UncertainODEProblem, x)
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nu = length(p.prob.u0)
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p.prob.θ .= x[nu .+ (1:length(p.prob.θ))]
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u = x[1:nu]
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end
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function (s::UncertainODESolver)(p::UncertainODEProblem, μs, t)
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N = nr_uncertainties(p)
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μs = map(1:N) do i
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u = setmean!(p, μs[:,i])
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u = s.solver(p.prob, u, t)[1]
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vcat(u, p.prob.θ)
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end
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μs = reduce(hcat, μs)
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μ = mean(μs,dims=2)
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Σ = Matrix((μs .- μ)*(μs .- μ)'/N)
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σ = sqrt.(diag(Σ))
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σ[p.u_idx] .= 0
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σ[p.θ_idx .+ length(p.prob.u0)] .= 0
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#μ .± σ, t+1
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μs, t+1
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end
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function solve(p::UncertainODEProblem, solver::UncertainODESolver)
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t = p.prob.tspan[1]; u = p.U0
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us = [u]; ts = [t]
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while t < prob.tspan[2]
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(u,t) = solver(p, u, t)
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push!(us,u)
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push!(ts,t)
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end
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ts, reduce(hcat,us)
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end
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uprob = UncertainODEProblem(prob)
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solver = UncertainODESolver(RK2(0.2))
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t, X = solve(uprob,solver)
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# function solve(f,x0::AbstractVector,sqΣ0, θ,dt,N)
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# n = length(x0)
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# n2 = 2*length(x0)
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# Qp = sqrt(n)*[I(n) -I(n)]
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#
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# X = hcat([zero(x0) for i=1:N]...)
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# S = hcat([zero(x0) for i=1:N]...)
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# X[:,1]=x0
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# Xp = x0 .+ sqΣ0*Qp
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# sqΣ = sqΣ0
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# Σ = sqΣ* sqΣ'
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# S[:,1]= diag(Σ)
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# for t=1:N-1
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# for i=1:n2 # all quadrature points
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# Xp[:,i].=Xp[:,i] + dt*f(Xp[:,i],θ)
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# end
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# mXp=mean(Xp,dims=2)
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# X[:,t+1]=mXp
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# Σ=Matrix((Xp.-mXp)*(Xp.-mXp)'/n2)
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# S[:,t+1]=sqrt.(diag(Σ))
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# # @show Σ
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#
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# end
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# X,S
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# end
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