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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 `~/github-runners/deepsea4-27/_work/DiffEqDevDocs.jl/DiffEqDevDocs.jl/docs/Project.toml`
  [fa972c1a] DiffEqDevDocs v1.0.0 `~/github-runners/deepsea4-27/_work/DiffEqDevDocs.jl/DiffEqDevDocs.jl`
  [f3b72e0c] DiffEqDevTools v2.49.0
  [e30172f5] Documenter v1.16.1
  [1dea7af3] OrdinaryDiffEq v6.105.0
and using this machine and Julia version.
Julia Version 1.12.3
Commit 966d0af0fdf (2025-12-15 11:20 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7513 32-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 128 virtual cores)
Environment:
  JULIA_DEPOT_PATH = /home/chrisrackauckas/github-runners/deepsea4-27/.julia
A more complete overview of all dependencies and their versions is also provided.
Status `~/github-runners/deepsea4-27/_work/DiffEqDevDocs.jl/DiffEqDevDocs.jl/docs/Manifest.toml`
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  [fa972c1a] DiffEqDevDocs v1.0.0 `~/github-runners/deepsea4-27/_work/DiffEqDevDocs.jl/DiffEqDevDocs.jl`
  [f3b72e0c] DiffEqDevTools v2.49.0
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  [163ba53b] DiffResults v1.1.0
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  [a4df4552] FastPower v1.3.0
  [1a297f60] FillArrays v1.15.0
  [6a86dc24] FiniteDiff v2.29.0
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  [f6369f11] ForwardDiff v1.3.1
  [069b7b12] FunctionWrappers v1.1.3
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  [682c06a0] JSON v1.3.0
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  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [d0879d2d] MarkdownAST v0.1.2
  [bb5d69b7] MaybeInplace v0.1.4
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  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.10.0
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.13.0
  [be0214bd] NonlinearSolveBase v2.9.0
  [5959db7a] NonlinearSolveFirstOrder v1.11.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.12.0
  [26075421] NonlinearSolveSpectralMethods v1.6.0
  [429524aa] Optim v1.13.3
  [bac558e1] OrderedCollections v1.8.1
  [1dea7af3] OrdinaryDiffEq v6.105.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.8.0
  [6ad6398a] OrdinaryDiffEqBDF v1.13.0
  [bbf590c4] OrdinaryDiffEqCore v2.3.0
  [50262376] OrdinaryDiffEqDefault v1.11.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.21.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.7.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.11.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.12.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.19.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.7.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.8.0
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.8.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.10.0
  [521117fe] OrdinaryDiffEqLinear v1.9.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.9.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.10.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.18.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.7.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.9.0
  [5b33eab2] OrdinaryDiffEqPRK v1.7.0
  [04162be5] OrdinaryDiffEqQPRK v1.7.0
  [af6ede74] OrdinaryDiffEqRKN v1.8.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.21.0
  [2d112036] OrdinaryDiffEqSDIRK v1.10.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.10.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.9.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.7.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.10.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.8.0
  [79d7bb75] OrdinaryDiffEqVerner v1.9.0
  [90014a1f] PDMats v0.11.37
  [69de0a69] Parsers v2.8.3
  [e409e4f3] PoissonRandom v0.4.7
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
⌅ [d236fae5] PreallocationTools v0.4.34
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.1
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [817f1d60] ReTestItems v1.35.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.42.1
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.2.0
  [79098fc4] Rmath v0.9.0
  [47965b36] RootedTrees v2.24.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.16
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.131.0
  [19f34311] SciMLJacobianOperators v0.1.12
  [a6db7da4] SciMLLogging v1.8.0
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  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
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  [ade2ca70] Dates v1.11.0
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  [d6f4376e] Markdown v1.11.0
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  [8dfed614] Test v1.11.0
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  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
You can also download the "https://github.com/SciML/DiffEqDevDocs.jl/tree/gh-pages/v1.0.0/assets/Manifest.toml"">manifest file and the "https://github.com/SciML/DiffEqDevDocs.jl/tree/gh-pages/v1.0.0/assets/Project.toml"">project file.