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SciML Scientific Machine Learning Developer Documentation

This is the developer documentation and Contributor's Guide for the SciML ecosystem. It explains the common interface and some the package internals to help developers contribute.

If you have any questions, or just want to chat about solvers/using the package, please feel free to use the Gitter channel. For bug reports, feature requests, etc., please submit an issue.

Overview

The SciML ecosystem is built around the common interface. The common interface is a type-based interface where users define problems as a type, and solvers plug into the ecosystem by defining an algorithm to give a new dispatch to

__solve(prob, alg; kwargs...)
__init(prob, alg; kwargs...)

There is a top level solve and init function which is in DiffEqBase.jl that handles distribution and function input (along with extra warnings) before sending the problems to the packages.

There is then an ecosystem of add-on components which use the common solver interface to add analysis tools for differential equations.

Contributing to the Ecosystem

There are many ways to help the ecosystem. One way you can contribute is to give pull requests (PRs) to existing packages. Another way to contribute is to add your own package to the ecosystem. Adding your own package to the ecosystem allows you to keep executive control and licensing over your methods, but allows users of DifferentialEquations.jl to use your methods via the common interface, and makes your package compatible with the add-on tools (sensitivity analysis, parameter estimation, etc). Note that, in order for the method to be used as a default, one is required to move their package to the SciML organization so that way common maintenance (such as fixing deprecation warnings, updating tests to newer versions, and emergency fixes / disabling) can be allowed by SciML members. However, the lead developer of the package maintains administrative control, and thus any change to the core algorithms by other SciML members will only be given through PRs.

Even if you don't have the time to contribute new solver algorithms or add-on tools, there's always ways to help! Improved plot recipes and new series recipes are always nice to add more default plots. It is always helpful to have benchmarks between different algorithms to see "which is best". Adding examples IJulia notebooks to DiffEqTutorials.jl is a good way to share knowledge about DifferentialEquations.jl. Also, please feel free to comb through the solvers and look for ways to make them more efficient. Lastly, the documentation could always use improvements. If you have any questions on how to help, just ask them in the Gitter!

Code of Conduct

All contributors must adhere to the NumFOCUS Code of Conduct. Treat everyone with respect. Failure to comply will result in individuals being banned from the community.

Contributor Guide

Algorithm Development Tools

The following algorithm development tools are provided by DiffEqDevTools.jl

Internal Documentation

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl/docs/Project.toml`
  [f3b72e0c] DiffEqDevTools v3.0.0 `../lib/DiffEqDevTools`
  [e30172f5] Documenter v1.17.0
  [1dea7af3] OrdinaryDiffEq v7.0.0 `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl`
  [08082164] OrdinaryDiffEqAMF v2.0.0 `../lib/OrdinaryDiffEqAMF`
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v2.0.0 `../lib/OrdinaryDiffEqAdamsBashforthMoulton`
  [6ad6398a] OrdinaryDiffEqBDF v2.0.0 `../lib/OrdinaryDiffEqBDF`
  [50262376] OrdinaryDiffEqDefault v2.0.0 `../lib/OrdinaryDiffEqDefault`
  [9286f039] OrdinaryDiffEqExplicitRK v2.0.0 `../lib/OrdinaryDiffEqExplicitRK`
  [e0540318] OrdinaryDiffEqExponentialRK v2.0.0 `../lib/OrdinaryDiffEqExponentialRK`
  [becaefa8] OrdinaryDiffEqExtrapolation v2.0.0 `../lib/OrdinaryDiffEqExtrapolation`
  [5960d6e9] OrdinaryDiffEqFIRK v2.0.0 `../lib/OrdinaryDiffEqFIRK`
  [101fe9f7] OrdinaryDiffEqFeagin v2.0.0 `../lib/OrdinaryDiffEqFeagin`
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v2.0.0 `../lib/OrdinaryDiffEqHighOrderRK`
  [9f002381] OrdinaryDiffEqIMEXMultistep v2.0.0 `../lib/OrdinaryDiffEqIMEXMultistep`
  [521117fe] OrdinaryDiffEqLinear v2.0.0 `../lib/OrdinaryDiffEqLinear`
  [1344f307] OrdinaryDiffEqLowOrderRK v2.0.0 `../lib/OrdinaryDiffEqLowOrderRK`
  [b0944070] OrdinaryDiffEqLowStorageRK v2.0.0 `../lib/OrdinaryDiffEqLowStorageRK`
  [c9986a66] OrdinaryDiffEqNordsieck v2.0.0 `../lib/OrdinaryDiffEqNordsieck`
  [5dd0a6cf] OrdinaryDiffEqPDIRK v2.0.0 `../lib/OrdinaryDiffEqPDIRK`
  [5b33eab2] OrdinaryDiffEqPRK v2.0.0 `../lib/OrdinaryDiffEqPRK`
  [04162be5] OrdinaryDiffEqQPRK v2.0.0 `../lib/OrdinaryDiffEqQPRK`
  [af6ede74] OrdinaryDiffEqRKN v2.0.0 `../lib/OrdinaryDiffEqRKN`
  [43230ef6] OrdinaryDiffEqRosenbrock v2.0.0 `../lib/OrdinaryDiffEqRosenbrock`
  [2d112036] OrdinaryDiffEqSDIRK v2.0.0 `../lib/OrdinaryDiffEqSDIRK`
  [669c94d9] OrdinaryDiffEqSSPRK v2.0.0 `../lib/OrdinaryDiffEqSSPRK`
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v2.0.0 `../lib/OrdinaryDiffEqStabilizedIRK`
  [358294b1] OrdinaryDiffEqStabilizedRK v2.0.0 `../lib/OrdinaryDiffEqStabilizedRK`
  [fa646aed] OrdinaryDiffEqSymplecticRK v2.0.0 `../lib/OrdinaryDiffEqSymplecticRK`
  [b1df2697] OrdinaryDiffEqTsit5 v2.0.0 `../lib/OrdinaryDiffEqTsit5`
  [79d7bb75] OrdinaryDiffEqVerner v2.0.0 `../lib/OrdinaryDiffEqVerner`
and using this machine and Julia version.
Julia Version 1.12.6
Commit 15346901f00 (2026-04-09 19:20 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
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  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v2.0.0 `../lib/OrdinaryDiffEqAdamsBashforthMoulton`
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  [9286f039] OrdinaryDiffEqExplicitRK v2.0.0 `../lib/OrdinaryDiffEqExplicitRK`
  [e0540318] OrdinaryDiffEqExponentialRK v2.0.0 `../lib/OrdinaryDiffEqExponentialRK`
  [becaefa8] OrdinaryDiffEqExtrapolation v2.0.0 `../lib/OrdinaryDiffEqExtrapolation`
  [5960d6e9] OrdinaryDiffEqFIRK v2.0.0 `../lib/OrdinaryDiffEqFIRK`
  [101fe9f7] OrdinaryDiffEqFeagin v2.0.0 `../lib/OrdinaryDiffEqFeagin`
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v2.0.0 `../lib/OrdinaryDiffEqHighOrderRK`
  [9f002381] OrdinaryDiffEqIMEXMultistep v2.0.0 `../lib/OrdinaryDiffEqIMEXMultistep`
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  [1344f307] OrdinaryDiffEqLowOrderRK v2.0.0 `../lib/OrdinaryDiffEqLowOrderRK`
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  [5dd0a6cf] OrdinaryDiffEqPDIRK v2.0.0 `../lib/OrdinaryDiffEqPDIRK`
  [5b33eab2] OrdinaryDiffEqPRK v2.0.0 `../lib/OrdinaryDiffEqPRK`
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  [e3e12d00] OrdinaryDiffEqStabilizedIRK v2.0.0 `../lib/OrdinaryDiffEqStabilizedIRK`
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  [b1df2697] OrdinaryDiffEqTsit5 v2.0.0 `../lib/OrdinaryDiffEqTsit5`
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
You can also download the "https://github.com/SciML/OrdinaryDiffEq.jl/tree/gh-pages/v7.0.0/assets/Manifest.toml"">manifest file and the "https://github.com/SciML/OrdinaryDiffEq.jl/tree/gh-pages/v7.0.0/assets/Project.toml"">project file.