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

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SciMLBenchmarks.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.

Interactive Notebooks

To run the tutorials interactively via Jupyter notebooks and benchmark on your own machine, install the package and open the tutorials like:

]add ""
using SciMLBenchmarks

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


All of the files are generated from the Weave.jl files in the benchmarks folder. To run the generation process, do for example:

]activate SciMLBenchmarks # Get all of the packages
using SciMLBenchmarks

To generate all of the files in a folder, for example, run:


To generate all of the notebooks, do:


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.