SciMLExpectations.jl: Expectated Values of Simulations and Uncertainty Quantification

This package is still under heavy construction. Use at your own risk!

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 stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Example

using SciMLExpectations, OrdinaryDiffEq, Distributions, IntegralsCubature

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])
analytical

julia> analytical
2-element Vector{Float64}:
  1.5433991194037804
 -1.120209038276938

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

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 =#