SciMLBenchmarksOutput.jl: Benchmarks for Scientific Machine Learning (SciML) and Differential Equation Solver Software

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SciMLBenchmarksOutput.jl holds webpages, pdfs, and notebooks showing the benchmarks for the SciML Scientific Machine Learning Software ecosystem, including cross-language benchmarks of differential equation solvers and methods for parameter estimation, training universal differential equations (and subsets like neural ODEs), and more.

Currently, only the html, pdf, and markdown versions should be viewed here. To use the interactive notebooks and scripts, see, since the interactive components require the environments contained in that repo.

Table of Contents

The following tests were developed for the paper Adaptive Methods for Stochastic Differential Equations via Natural Embeddings and Rejection Sampling with Memory. These notebooks track their latest developments.

Current Summary

The following is a quick summary of the benchmarks. These paint broad strokes over the set of tested equations and some specific examples may differ.

Non-Stiff ODEs

Stiff ODEs

Dynamical ODEs

Non-Stiff SDEs

Stiff SDEs

Non-Stiff DDEs

Stiff DDEs

Parameter Estimation


Each of the benchmarks displays the computer characteristics at the bottom of the benchmark. Since performance-necessary computations are normally performed on compute clusters, the official benchmarks use a workstation with an Intel Xeon CPU E5-2680 v4 @ 2.40GHz to match the performance characteristics of a standard node in a high performance computing (HPC) cluster or cloud computing setup.