sharanry / SciMLExpectations.jl

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

SciMLExpectations.jl: Expectated Values of Simulations and Uncertainty Quantification

SciMLExpectations.jl is a package for quantifying the uncertainties of simulations by calculating the expectations of observables with respect to input uncertainties. Its goal is to make it fast and easy to compute solution moments in a differentiable way in order to enable fast optimization under uncertainty.

Tutorials and Documentation

For information on using the package, see the SciMLExpectations section of the SciML docs. For information on specific previous versions of this package, see the see the stable SciMLExpectations-only documentation.

Example

using SciMLExpectations, OrdinaryDiffEq, Distributions, Integrals,
      IntegralsCubature, ComponentArrays, Random

function eom!(du, u, p, t, A)
    du .= A * u
end

u0 = [1.0, 1.0]
tspan = (0.0, 3.0)
p = [1.0; 2.0]
A = [0.0 1.0; -p[1] -p[2]]
prob = ODEProblem((du, u, p, t) -> eom!(du, u, p, t, A), u0, tspan, p)
u0s_dist = (Uniform(1, 10), truncated(Normal(3.0, 1), 0.0, 6.0))
gd = GenericDistribution(u0s_dist...)
cov(x, u, p) = x, p

sm = SystemMap(prob, Tsit5(), save_everystep=false)

analytical = (exp(A * tspan[end]) * [mean(d) for d in u0s_dist])

g(sol, p) = sol[:, end]
exprob = ExpectationProblem(sm, g, cov, gd; nout=length(u0))
sol = solve(exprob, Koopman(); quadalg=CubatureJLh(),
    ireltol=1e-3, iabstol=1e-3)

# Expectation of the states 1 and 2 at the final time point
sol.u

#=
2-element Vector{Float64}:
  1.5433860531082695
 -1.1201922503747408
=#

# Approximate error on the expectation
sol.resid
#=
2-element Vector{Float64}:
 7.193424502016654e-5
 5.2074632876847327e-5
=#