SciML Open Source Scientific Machine Learning

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190 repositories

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
•227•1.5k•385•90•Updated Jul 1, 2025Jul 1, 2025
SurrogatesBase.jl
Public
Basically just a surrogate in disguise
Julia
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MIT License
•4•5•0•0•Updated Jul 1, 2025Jul 1, 2025
SciMLBook
Public
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
performance-engineering parallelism neural-networks gpu-computing numerical-methods lecture-notes neural-ode neural-sde stiff-equations scientific-simulators
HTML
•351•1.9k•10•2•Updated Jul 1, 2025Jul 1, 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 1, 2025Jul 1, 2025
ModelOrderReduction.jl
Public
High-level model-order reduction to automate the acceleration of large-scale simulations
hpc partial-differential-equations model-order-reduction julia differential-equations scientific-machine-learning sciml
Julia
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MIT License
•6•39•19•27•Updated Jul 1, 2025Jul 1, 2025
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
•221•1.1k•108•22•Updated Jul 1, 2025Jul 1, 2025
ADTypes.jl
Public
Repository for automatic differentiation backend types
julia automatic-differentiation autodiff
Julia
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MIT License
•15•51•7•4•Updated Jul 1, 2025Jul 1, 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•489•94•20•Updated Jul 1, 2025Jul 1, 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
•19•122•11•6•Updated Jul 1, 2025Jul 1, 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
•47•269•34•8•Updated Jun 30, 2025Jun 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 ordinary-differential-equations adaptive differentialequations event-handling hacktoberfest julia ode differential-equations scientific-machine-learning
Julia
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Other
•225•594•326•47•Updated Jun 30, 2025Jun 30, 2025
QuasiMonteCarlo.jl
Public
Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)
parameter-estimation quasi-monte-carlo physics-informed-learning julia scientific-machine-learning sciml
Julia
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MIT License
•26•113•16•0•Updated Jun 29, 2025Jun 29, 2025
DataInterpolations.jl
Public
A library of data interpolation and smoothing functions
Julia
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MIT License
•52•250•30•6•Updated Jun 29, 2025Jun 29, 2025
NDInterpolations.jl
Public
Interpolation of arbitrarily high dimensional array data
interpolation sciml
Julia
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MIT License
•0•6•13•1•Updated Jun 29, 2025Jun 29, 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•27•5•Updated Jun 29, 2025Jun 29, 2025
RuntimeGeneratedFunctions.jl
Public
Functions generated at runtime without world-age issues or overhead
julia
Julia
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MIT License
•16•105•14•0•Updated Jun 28, 2025Jun 28, 2025
PoissonRandom.jl
Public
Fast Poisson Random Numbers in pure Julia for scientific machine learning (SciML)
high-performance-computing poisson poisson-distribution poisson-processes scientific-machine-learning sciml tau-leaping julia
Julia
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Other
•6•18•1•0•Updated Jun 28, 2025Jun 28, 2025
EllipsisNotation.jl
Public
Julia-based implementation of ellipsis array indexing notation `..`
arrays julia julia-language julialang
Julia
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Other
•14•96•2•0•Updated Jun 28, 2025Jun 28, 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
•98•328•26•39•Updated Jun 28, 2025Jun 28, 2025
FindFirstFunctions.jl
Public
Faster `findfirst(==(val), dense_vector)`.
Julia
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MIT License
•3•10•3•0•Updated Jun 27, 2025Jun 27, 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•336•55•11•Updated Jun 27, 2025Jun 27, 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
•53•59•7•0•Updated Jun 27, 2025Jun 27, 2025
CellMLToolkit.jl
Public
CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.
systems-biology physiology cellml julia ode differential-equations scientific-machine-learning sciml
Julia
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Other
•17•67•9•1•Updated Jun 27, 2025Jun 27, 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
•76•354•105•6•Updated Jun 27, 2025Jun 27, 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
•97•785•81•19•Updated Jun 27, 2025Jun 27, 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
•16•121•3•0•Updated Jun 27, 2025Jun 27, 2025
SciMLStructures.jl
Public
A structure interface for SciML to give queryable properties from user data and parameters
api interfaces
Julia
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MIT License
•5•9•0•0•Updated Jun 26, 2025Jun 26, 2025
BaseModelica.jl
Public
Importers for the BaseModelica standard into the Julia ModelingToolkit ecosystem
julia ode modelica differential-equations dae sciml symbolic-numeric-computing
Julia
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MIT License
•4•8•4•0•Updated Jun 26, 2025Jun 26, 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
•38•142•68•7•Updated Jun 26, 2025Jun 26, 2025
ParameterizedFunctions.jl
Public
A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications
parameters jacobian differential-equations scientific-machine-learning sciml
Julia
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Other
•16•77•1•0•Updated Jun 26, 2025Jun 26, 2025