Sparse Identification of Nonlinear Dynamics example in the tutorial fails #294
Description
Sparse Identification of Nonlinear Dynamics example in the Nonlinear Systems tutorial fails (in Julia 1.6.3). Below I copy all the code and only show the REPL output for the last (failing) line:
using DataDrivenDiffEq
using LinearAlgebra
using ModelingToolkit
using OrdinaryDiffEq
using Plots
using Random
using Symbolics: scalarize
Random.seed!(1111) # For the noise
# Create a nonlinear pendulum
function pendulum(u, p, t)
x = u[2]
y = -9.81sin(u[1]) - 0.3u[2]^3 -3.0*cos(u[1]) - 10.0*exp(-((t-5.0)/5.0)^2)
return [x;y]
end
u0 = [0.99π; -1.0]
tspan = (0.0, 15.0)
prob = ODEProblem(pendulum, u0, tspan)
sol = solve(prob, Tsit5(), saveat = 0.01)
# Create the data with additional noise
X = sol[:,:] + 0.1 .* randn(size(sol))
DX = similar(sol[:,:])
for (i, xi) in enumerate(eachcol(sol[:,:]))
DX[:,i] = pendulum(xi, [], sol.t[i])
end
ts = sol.t
prob = ContinuousDataDrivenProblem(X, ts, GaussianKernel(), U = (u,p,t)->[exp(-((t-5.0)/5.0)^2)], p = ones(2))
@variables u[1:2] c[1:1]
@parameters w[1:2]
u = scalarize(u)
c = scalarize(c)
w = scalarize(w)
h = Num[sin.(w[1].*u[1]);cos.(w[2].*u[1]); polynomial_basis(u, 5); c]
basis = Basis(h, u, parameters = w, controls = c)
λs = exp10.(-10:0.1:-1)
opt = STLSQ(λs)julia> res = solve(prob, basis, opt, progress = false, denoise = false, normalize = false, maxiter = 5000)
ERROR: BoundsError: attempt to access Sym{Vector{Real}, Base.ImmutableDict{DataType, Any}} at index [6]
Stacktrace:
[1] getindex(x::Sym{Vector{Real}, Base.ImmutableDict{DataType, Any}}, idx::Int64)
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/array-lib.jl:26
[2] scalarize(term::Sym{Vector{Real}, Base.ImmutableDict{DataType, Any}}, idx::Tuple{Int64})
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/arrays.jl:497
[3] scalarize(arr::Term{Real, Base.ImmutableDict{DataType, Any}})
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/arrays.jl:641
[4] scalarize(arr::Num)
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/arrays.jl:643
[5] (::Symbolics.var"#97#98"{Symbolics.Arr{Num, 1}})(i::Tuple{Int64})
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/arrays.jl:637
[6] iterate
@ ./generator.jl:47 [inlined]
[7] collect_to!(dest::Vector{Num}, itr::Base.Generator{Base.Iterators.ProductIterator{Tuple{UnitRange{Int64}}}, Symbolics.var"#97#98"{Symbolics.Arr{Num, 1}}}, offs::Int64, st::Tuple{Tuple{Int64, Int64}})
@ Base ./array.jl:728
[8] collect_to_with_first!(dest::Vector{Num}, v1::Num, itr::Base.Generator{Base.Iterators.ProductIterator{Tuple{UnitRange{Int64}}}, Symbolics.var"#97#98"{Symbolics.Arr{Num, 1}}}, st::Tuple{Tuple{Int64, Int64}})
@ Base ./array.jl:706
[9] collect(itr::Base.Generator{Base.Iterators.ProductIterator{Tuple{UnitRange{Int64}}}, Symbolics.var"#97#98"{Symbolics.Arr{Num, 1}}})
@ Base ./array.jl:687
[10] map(f::Function, A::Base.Iterators.ProductIterator{Tuple{UnitRange{Int64}}})
@ Base ./abstractarray.jl:2323
[11] scalarize(arr::Symbolics.Arr{Num, 1})
@ Symbolics ~/.julia/packages/Symbolics/Cmx10/src/arrays.jl:636
[12] build_parametrized_eqs(X::Matrix{Float64}, b::Basis)
@ DataDrivenDiffEq ~/.julia/packages/DataDrivenDiffEq/AGBrC/src/solution.jl:133
[13] build_solution(prob::DataDrivenProblem{Float64, false, DataDrivenDiffEq.Continuous}, Ξ::Matrix{Float64}, opt::STLSQ{Vector{Float64}}, b::Basis; eval_expression::Bool)
@ DataDrivenDiffEq ~/.julia/packages/DataDrivenDiffEq/AGBrC/src/solution.jl:167
[14] solve(p::DataDrivenProblem{Float64, false, DataDrivenDiffEq.Continuous}, b::Basis, opt::STLSQ{Vector{Float64}}; normalize::Bool, denoise::Bool, maxiter::Int64, round::Bool, eval_expression::Bool, kwargs::Base.Iterators.Pairs{Symbol, Bool, Tuple{Symbol}, NamedTuple{(:progress,), Tuple{Bool}}})
@ DataDrivenDiffEq ~/.julia/packages/DataDrivenDiffEq/AGBrC/src/solve/sindy.jl:53
[15] top-level scope
@ none:1