SciML Open Source Scientific Machine Learning

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192 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 ordinary-differential-equations adaptive differentialequations event-handling hacktoberfest julia ode differential-equations scientific-machine-learning
Julia
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Other
•231•601•328•53•Updated Jul 31, 2025Jul 31, 2025
NeuralOperators.jl
Public
DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia
Julia
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MIT License
•11•24•4•2•Updated Jul 30, 2025Jul 30, 2025
DASKR.jl
Public
Interface to DASKR, a differential algebraic system solver for the SciML scientific machine learning ecosystem
differential-equations differential-algebraic daskr differential-algebraic-equations scientific-machine-learning sciml differentialequations dae
Julia
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Other
•13•11•3•1•Updated Jul 30, 2025Jul 30, 2025
Sundials.jl
Public
Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner
julia clang ode ida differential-equations ordinary-differential-equations differentialequations dae sundials cvode
Julia
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BSD 2-Clause "Simplified" License
•78•210•37•5•Updated Jul 30, 2025Jul 30, 2025
ODEInterfaceDiffEq.jl
Public
Adds the common API onto ODEInterface classic Fortran methods for the SciML Scientific Machine Learning organization
julia radau rodas hairer scientific-machine-learning sciml differential-equations
Julia
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Other
•15•8•3•1•Updated Jul 30, 2025Jul 30, 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 symbolic dde ordinary-differential-equations sde pde dae stochastic-differential-equations delay-differential-equations
Julia
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Other
•230•1.5k•398•91•Updated Jul 30, 2025Jul 30, 2025
DiffEqBayes.jl
Public
Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning
dde stan ordinary-differential-equations sde dae stochastic-differential-equations neural-ode neural-differential-equations scientific-ml scientific-ai
Julia
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Other
•28•124•14•4•Updated Jul 30, 2025Jul 30, 2025
DiffEqGPU.jl
Public
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
dde differentialequations sde dae neural-ode neural-differential-equations gpu-parallelism gpu ode differential-equations
Julia
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MIT License
•35•307•28•5•Updated Jul 30, 2025Jul 30, 2025
NonlinearSolve.jl
Public
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
high-performance-computing factorization nonlinear-equations sparse-matrix sparse-matrices newton-raphson steady-state bracketing equilibrium newton-method
Julia
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MIT License
•49•270•36•10•Updated Jul 30, 2025Jul 30, 2025
BoundaryValueDiffEq.jl
Public
Boundary value problem (BVP) solvers for scientific machine learning (SciML)
gpu differential-equations differentialequations bvp neural-ode scientific-machine-learning neural-differential-equations neural-bvp sciml
Julia
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Other
•38•50•26•8•Updated Jul 30, 2025Jul 30, 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
•109•160•63•37•Updated Jul 30, 2025Jul 30, 2025
Static.jl
Public
Static types useful for dispatch and generated functions.
Julia
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MIT License
•17•59•17•5•Updated Jul 30, 2025Jul 30, 2025
SBMLToolkit.jl
Public
SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit
systems-biology ode differential-equations chemical-reaction-networks sbml gillespie-algorithm quantitative-systems-pharmacology sciml julia
Julia
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MIT License
•10•43•10•9•Updated Jul 30, 2025Jul 30, 2025
StructuralIdentifiability.jl
Public
Fast and automatic structural identifiability software for ODE systems
parameter-estimation differentialequations structural-identifiability julia
Julia
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MIT License
•20•123•9•8•Updated Jul 30, 2025Jul 30, 2025
sciml.ai
Public
The SciML Scientific Machine Learning Software Organization Website
machine-learning julia julia-language ode dde sde dae julialang franklin neural-ode
CSS
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MIT License
•55•59•7•3•Updated Jul 30, 2025Jul 30, 2025
Integrals.jl
Public
A common interface for quadrature and numerical integration for the SciML scientific machine learning organization
integration automatic-differentiation quadrature numerical-integration algorithmic-differentiation differentiable-programming julia julia-language julialang scientific-machine-learning
Julia
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MIT License
•31•236•22•6•Updated Jul 30, 2025Jul 30, 2025
StochasticDiffEq.jl
Public
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
random stochastic noise adaptive differentialequations sde stochastic-differential-equations sode ito hacktoberfest
Julia
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Other
•70•290•90•13•Updated Jul 30, 2025Jul 30, 2025
PreallocationTools.jl
Public
Tools for building non-allocating pre-cached functions in Julia, allowing for GC-free usage of automatic differentiation in complex codes
automatic-differentiation garbage-collection high-performance-computing differentiable-programming
Julia
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Other
•18•122•3•2•Updated Jul 30, 2025Jul 30, 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 distributed-computing factorization amg multigrid krylov-methods linear-solvers preconditioners sciml newton-krylov
Julia
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Other
•65•262•71•10•Updated Jul 30, 2025Jul 30, 2025
JumpProcesses.jl
Public
Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)
ssa stochastic sde gillespie jump-diffusion neural-ode neural-differential-equations scientific-ml scientific-ai hybrid-differential-equation
Julia
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Other
•37•142•69•9•Updated Jul 30, 2025Jul 30, 2025
DiffEqBase.jl
Public
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
dde partial-differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations delay-differential-equations hacktoberfest
Julia
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Other
•119•340•54•12•Updated Jul 30, 2025Jul 30, 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
•79•492•94•24•Updated Jul 30, 2025Jul 30, 2025
SciMLSensitivity.jl
Public
A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
ode dde differentialequations sde dae sensitivity-analysis hacktoberfest adjoint backpropogation neural-ode
Julia
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Other
•77•359•107•9•Updated Jul 30, 2025Jul 30, 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.
automatic-differentiation global-optimization hacktoberfest nonlinear-optimization convex-optimization algorithmic-differentiation mixed-integer-programming derivative-free-optimization sciml local-optimization
Julia
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MIT License
•99•787•92•12•Updated Jul 30, 2025Jul 30, 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•17•10•9•Updated Jul 30, 2025Jul 30, 2025
NeuralLyapunov.jl
Public
A library for searching for neural Lyapunov functions in Julia.
Julia
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Other
•1•4•2•3•Updated Jul 30, 2025Jul 30, 2025
LineSearch.jl
Public
Line Search Algorithms
Julia
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MIT License
•3•3•4•1•Updated Jul 30, 2025Jul 30, 2025
RootedTrees.jl
Public
A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)
julia differential-equations hacktoberfest runge-kutta rooted-trees scientific-machine-learning sciml
Julia
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MIT License
•17•37•8•5•Updated Jul 30, 2025Jul 30, 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)
sde stochastic-processes brownian-motion wiener-process noise-processes neural-sde differential-equations scientific-machine-learning sciml
Julia
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Other
•30•63•16•6•Updated Jul 30, 2025Jul 30, 2025
CurveFit.jl
Public
Least squares and curve fitting in Julia with speed and robustness
Julia
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Other
•17•86•6•2•Updated Jul 30, 2025Jul 30, 2025