SciML Open Source Scientific Machine Learning

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199 repositories

OrdinaryDiffEq.jl
Public
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
high-performance julia ode differential-equations ordinary-differential-equations adaptive differentialequations event-handling hacktoberfest scientific-machine-learning
Julia
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Other
•241•618•336•46•Updated Dec 29, 2025Dec 29, 2025
CurveFit.jl
Public
Least squares and curve fitting in Julia with speed and robustness
Julia
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Other
•22•89•6•4•Updated Dec 29, 2025Dec 29, 2025
GlobalSensitivity.jl
Public
Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia
julia julia-language ode morris-method differential-equations ordinary-differential-equations sensitivity-analysis global-sensitivity-analysis julialang gsa
Julia
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MIT License
•22•62•26•3•Updated Dec 29, 2025Dec 29, 2025
FiniteVolumeMethod.jl
Public
Solver for two-dimensional conservation equations using the finite volume method in Julia.
partial-differential-equations finite-volume-method
Julia
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MIT License
•7•48•1•5•Updated Dec 29, 2025Dec 29, 2025
SciMLBenchmarksOutput
Public
SciML-Bench Benchmarks for Scientific Machine Learning (SciML), Physics-Informed Machine Learning (PIML), and Scientific AI Performance
python performance r neural-network gpu julia matlab pytorch benchmarks differential-equations
HTML
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MIT License
•6•25•0•1•Updated Dec 29, 2025Dec 29, 2025
Surrogates.jl
Public
Surrogate modeling and optimization for scientific machine learning (SciML)
optimization julia automatic-differentiation high-performance-computing differential-equations surrogate surrogate-models surrogate-based-optimization surrogates scientific-machine-learning
Julia
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Other
•76•361•30•1•Updated Dec 29, 2025Dec 29, 2025
LineSearch.jl
Public
Line Search Algorithms
Julia
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MIT License
•4•3•6•2•Updated Dec 29, 2025Dec 29, 2025
LabelledArrays.jl
Public
Arrays which also have a label for each element for easy scientific machine learning (SciML)
arrays scientific-machine-learning sciml
Julia
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Other
•20•122•14•4•Updated Dec 29, 2025Dec 29, 2025
ComponentArrays.jl
Public
Arrays with arbitrarily nested named components.
machine-learning simulation optimization julia modeling array controls neural-networks arrays dynamical-systems
Julia
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MIT License
•39•338•70•11•Updated Dec 29, 2025Dec 29, 2025
CellMLToolkit.jl
Public
CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.
julia systems-biology ode differential-equations physiology cellml scientific-machine-learning sciml
Julia
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Other
•17•69•10•2•Updated Dec 29, 2025Dec 29, 2025
PDEBase.jl
Public
Common types and interface for discretizers of ModelingToolkit PDESystems.
Julia
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MIT License
•9•13•10•2•Updated Dec 29, 2025Dec 29, 2025
HighDimPDE.jl
Public
A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality
machine-learning deep-learning julia neural-networks differential-equations pde pde-solver scientific-machine-learning sciml feynman-kac
Julia
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Other
•10•83•6•7•Updated Dec 29, 2025Dec 29, 2025
MinimallyDisruptiveCurves.jl
Public
Finds relationships between the parameters of a mathematical model
Julia
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MIT License
•5•51•2•0•Updated Dec 29, 2025Dec 29, 2025
DiffEqPhysics.jl
Public
A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)
fast ode differential-equations ordinary-differential-equations differentialequations hamiltonian second-order-differential-equations scientific-machine-learning sciml
Julia
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Other
•19•52•7•1•Updated Dec 29, 2025Dec 29, 2025
DiffEqFinancial.jl
Public
Differential equation problem specifications and scientific machine learning for common financial models
financial stochastic differential-equations differentialequations sde stochastic-differential-equations black-scholes black-scholes-merton scientific-machine-learning sciml
Julia
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Other
•14•31•2•1•Updated Dec 29, 2025Dec 29, 2025
SimpleNorm.jl
Public
Implementation of a norm function without LinearAlgebra.jl / BLAS / LAPACK
Julia
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MIT License
•1•1•0•0•Updated Dec 29, 2025Dec 29, 2025
LightweightStats.jl
Public
Lightweight Julia package for basic statistical functions with minimal dependencies
Julia
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MIT License
•1•3•1•0•Updated Dec 29, 2025Dec 29, 2025
SciMLBenchmarks.jl
Public
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
python benchmark ai julia matlab pytorch ode partial-differential-equations differential-equations differentialequations
MATLAB
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MIT License
•104•334•20•69•Updated Dec 29, 2025Dec 29, 2025
SparseMatrixIdentification.jl
Public
Julia
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MIT License
•1•2•4•1•Updated Dec 29, 2025Dec 29, 2025
SBMLToolkit.jl
Public
SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit
julia systems-biology ode differential-equations chemical-reaction-networks sbml gillespie-algorithm quantitative-systems-pharmacology sciml
Julia
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MIT License
•10•44•10•9•Updated Dec 29, 2025Dec 29, 2025
ADTypes.jl
Public
Repository for automatic differentiation backend types
julia automatic-differentiation autodiff
Julia
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MIT License
•15•60•9•4•Updated Dec 29, 2025Dec 29, 2025
GlobalDiffEq.jl
Public
Differential equation solvers with global error estimation
Julia
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MIT License
•6•11•6•1•Updated Dec 29, 2025Dec 29, 2025
ModelingToolkit.jl
Public
An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
computer-algebra optimization julia ode symbolic dde differential-equations ordinary-differential-equations sde pde
Julia
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Other
•238•1.6k•436•102•Updated Dec 29, 2025Dec 29, 2025
SciMLBase.jl
Public
The Base interface of the SciML ecosystem
julia ode dde ordinary-differential-equations differentialequations sde dae scientific-machine-learning sciml
Julia
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MIT License
•114•167•69•29•Updated Dec 29, 2025Dec 29, 2025
DiffEqBase.jl
Public
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
ode dde partial-differential-equations differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations
Julia
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Other
•122•348•57•15•Updated Dec 29, 2025Dec 29, 2025
QuantumNLDiffEq.jl
Public
Julia
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MIT License
•5•18•4•1•Updated Dec 29, 2025Dec 29, 2025
DiffEqNoiseProcess.jl
Public
A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)
differential-equations sde stochastic-processes brownian-motion wiener-process noise-processes scientific-machine-learning neural-sde sciml
Julia
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Other
•31•63•16•3•Updated Dec 29, 2025Dec 29, 2025
SciMLLogging.jl
Public
A logging system for SciML
Julia
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MIT License
•5•8•2•1•Updated Dec 29, 2025Dec 29, 2025
MATLABDiffEq.jl
Public
Common interface bindings for the MATLAB ODE solvers via MATLAB.jl for the SciML Scientific Machine Learning ecosystem
matlab scientific-machine-learning sciml
Julia
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Other
•13•20•0•1•Updated Dec 29, 2025Dec 29, 2025
BaseModelica.jl
Public
Importers for the BaseModelica standard into the Julia ModelingToolkit ecosystem
julia ode modelica differential-equations dae sciml symbolic-numeric-computing
Python
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MIT License
•4•8•8•1•Updated Dec 29, 2025Dec 29, 2025