https://github.com/sciml/scimlexpectations.jl

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
https://github.com/sciml/scimlexpectations.jl

differential-equations differentialequations integration julia ode scientific-machine-learning sciml uncertainty-quantification uq

Last synced: 28 days ago
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Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

• Host: GitHub
• URL: https://github.com/sciml/scimlexpectations.jl
• Owner: SciML
• License: other
• Created: 2016-11-02T18:17:13.000Z (almost 9 years ago)
• Default Branch: master
• Last Pushed: 2025-08-18T21:15:44.000Z (about 2 months ago)
• Last Synced: 2025-09-05T09:55:07.028Z (about 1 month ago)
• Topics: differential-equations, differentialequations, integration, julia, ode, scientific-machine-learning, sciml, uncertainty-quantification, uq
• Language: Julia
• Homepage: https://docs.sciml.ai/SciMLExpectations/stable/
• Size: 70.1 MB
• Stars: 69
• Watchers: 7
• Forks: 20
• Open Issues: 34
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md
  • Citation: CITATION.bib

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README

          
# SciMLExpectations.jl: Expectated Values of Simulations and Uncertainty Quantification

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#### 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](https://docs.sciml.ai/SciMLExpectations/stable/). Use the

[in-development documentation](https://docs.sciml.ai/SciMLExpectations/dev/) for the version of

the documentation, which contains the unreleased features.

### Example

```julia

using SciMLExpectations, OrdinaryDiffEq, Distributions, Cubature

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

```

```julia

g(sol, p) = sol[:, end]

exprob = ExpectationProblem(sm, g, cov, gd)

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

=#

```

```