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SciML Open Source Scientific Machine Learning

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199 repositories

NonlinearSolve.jl
Public
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
julia high-performance-computing differential-equations factorization nonlinear-equations sparse-matrix sparse-matrices newton-raphson steady-state bracketing
Julia
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MIT License
•61•285•42•16•Updated Jan 1, 2026Jan 1, 2026
ModelingToolkitNeuralNets.jl
Public
Symbolic-Numeric Neural DAEs and Universal Differential Equations for Automating Scientific Machine Learning (SciML)
machine-learning julia neural-networks ude neural-ode sciml symbolic-numerics
Julia
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MIT License
•6•39•7•3•Updated Jan 1, 2026Jan 1, 2026
CommonSolve.jl
Public
A common solve function for scientific machine learning (SciML) and beyond
interface scientific-machine-learning sciml composibility
Julia
•8•26•0•0•Updated Jan 1, 2026Jan 1, 2026
SparseMatrixIdentification.jl
Public
Julia
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MIT License
•1•4•0•1•Updated Jan 1, 2026Jan 1, 2026
NeuralPDE.jl
Public
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
machine-learning neural-network ode neural-networks partial-differential-equations differential-equations ordinary-differential-equations differentialequations pde pinn
Julia
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Other
•228•1.2k•110•23•Updated Dec 31, 2025Dec 31, 2025
SciMLExpectations.jl
Public
Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
integration julia ode differential-equations differentialequations uncertainty-quantification uq scientific-machine-learning sciml
Julia
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Other
•20•71•29•4•Updated Dec 31, 2025Dec 31, 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•2•Updated Dec 31, 2025Dec 31, 2025
ReservoirComputing.jl
Public
Reservoir computing utilities for scientific machine learning (SciML)
machine-learning julia rnn differential-equations echo-state-networks reservoir-computing scientific-machine-learning sciml
Julia
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MIT License
•42•222•32•4•Updated Dec 31, 2025Dec 31, 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•362•29•1•Updated Dec 31, 2025Dec 31, 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•11•3•Updated Dec 31, 2025Dec 31, 2025
LinearSolve.jl
Public
LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.
gpu julia linear-algebra distributed-computing differential-equations factorization amg multigrid krylov-methods linear-solvers
Julia
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Other
•80•276•70•7•Updated Dec 31, 2025Dec 31, 2025
IRKGaussLegendre.jl
Public
Implicit Runge-Kutta Gauss-Legendre 16th order (Julia)
Julia
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MIT License
•10•28•3•1•Updated Dec 31, 2025Dec 31, 2025
PDEBase.jl
Public
Common types and interface for discretizers of ModelingToolkit PDESystems.
Julia
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MIT License
•9•13•10•4•Updated Dec 31, 2025Dec 31, 2025
SymbolicIndexingInterface.jl
Public
A general interface for symbolic indexing of SciML objects used in conjunction with Domain-Specific Languages
dsl indexing symbolic domain-specific-language symbolic-computation scientific-machine-learning sciml high-level-interfaces acausal-modeling
Julia
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MIT License
•9•19•11•9•Updated Dec 31, 2025Dec 31, 2025
DiffEqCallbacks.jl
Public
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
julia callback ode dde differential-equations sde dae neural-ode scientific-machine-learning sciml
Julia
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Other
•53•100•23•4•Updated Dec 31, 2025Dec 31, 2025
DataInterpolationsND.jl
Public
Interpolation of arbitrarily high dimensional array data
interpolation sciml
Julia
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MIT License
•7•27•23•5•Updated Dec 31, 2025Dec 31, 2025
BridgeDiffEq.jl
Public
A thin wrapper over Bridge.jl for the SciML scientific machine learning common interface, enabling new methods for neural stochastic differential equations (neural SDEs)
ode bridge differential-equations sde neural-ode scientific-machine-learning neural-sde sciml
Julia
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Other
•8•6•4•0•Updated Dec 31, 2025Dec 31, 2025
Optimization.jl
Public
Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable interface.
optimization julia automatic-differentiation global-optimization hacktoberfest nonlinear-optimization convex-optimization algorithmic-differentiation mixed-integer-programming scientific-machine-learning
Julia
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MIT License
•96•809•101•8•Updated Dec 31, 2025Dec 31, 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•103•Updated Dec 31, 2025Dec 31, 2025
SBMLToolkitTestSuite.jl
Public
Functions to run the SBML Test Suite with SBMLToolkit, create logs and create reports for the SBML Test Suite Database
Julia
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MIT License
•1•6•0•7•Updated Dec 31, 2025Dec 31, 2025
DiffEqParamEstim.jl
Public
Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions
estimation ode dde differential-equations parameter-estimation ordinary-differential-equations differentialequations sde dae stochastic-differential-equations
Julia
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Other
•33•63•16•8•Updated Dec 31, 2025Dec 31, 2025
ModelOrderReduction.jl
Public
High-level model-order reduction to automate the acceleration of large-scale simulations
hpc julia partial-differential-equations differential-equations model-order-reduction scientific-machine-learning sciml
Julia
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MIT License
•6•42•19•8•Updated Dec 31, 2025Dec 31, 2025
Catalyst.jl
Public
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
simulation biology dsl julia systems-biology ode reaction-network differential-equations sde chemical-reactions
Julia
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Other
•80•503•104•35•Updated Dec 31, 2025Dec 31, 2025
SciMLBook
Public
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
performance-engineering parallelism neural-networks differential-equations gpu-computing numerical-methods lecture-notes neural-ode scientific-machine-learning neural-sde
HTML
•360•2k•12•1•Updated Dec 31, 2025Dec 31, 2025
DiffEqGPU.jl
Public
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
gpu ode dde differential-equations differentialequations sde dae neural-ode scientific-machine-learning neural-differential-equations
Julia
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MIT License
•38•310•28•3•Updated Dec 30, 2025Dec 30, 2025
MultiScaleArrays.jl
Public
A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations
julia models automatic-differentiation ode dde differential-equations differentialequations sde dae multiscale
Julia
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Other
•17•77•4•2•Updated Dec 30, 2025Dec 30, 2025
MethodOfLines.jl
Public
Automatic Finite Difference PDE solving with Julia SciML
julia parallel-computing high-performance-computing partial-differential-equations pde symbolic-computation finite-difference-method scientific-ml sciml
Julia
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MIT License
•38•195•103•19•Updated Dec 30, 2025Dec 30, 2025
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
•242•617•337•46•Updated Dec 30, 2025Dec 30, 2025
SymbolicAnalysis.jl
Public
Symbolics-based function property propagation for optimization
Julia
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MIT License
•3•20•2•6•Updated Dec 30, 2025Dec 30, 2025
ODEInterfaceDiffEq.jl
Public
Adds the common API onto ODEInterface classic Fortran methods for the SciML Scientific Machine Learning organization
julia differential-equations radau rodas hairer scientific-machine-learning sciml
Julia
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Other
•18•8•3•0•Updated Dec 30, 2025Dec 30, 2025