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SciML /DifferentialEquations.jl

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Star3k

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

python r julia ode dde scientific dynamical-systems differential-equations differentialequations sde dae spde stochastic-differential-equations delay-differential-equations numerical stochastic-processes differential-algebraic-equations scientific-machine-learning neural-differential-equations sciml

UpdatedOct 23, 2025
Julia

SciML /SciMLBook

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Star1.9k

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 stiff-equations scientific-simulators sciml

UpdatedSep 21, 2025
HTML

SciML /ModelingToolkit.jl

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Star1.6k

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 dae stochastic-differential-equations delay-differential-equations symbolic-computation nonlinear-programming equation-based scientific-machine-learning sciml symbolic-numerics acausal

UpdatedNov 6, 2025
Julia

SciML /NeuralPDE.jl

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Star1.1k

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 scientific-machine-learning neural-differential-equations scientific-ml scientific-ai sciml

UpdatedNov 3, 2025
Julia

pdebench /PDEBench

Star989

PDEBench: An Extensive Benchmark for Scientific Machine Learning

benchmark machine-learning ai deep-learning simulation pytorch scientific-computing neural-networks scientific partial-differential-equations fluid-dynamics jax navier-stokes-equations sciml autoregressive-models physics-informed-neural-networks neural-operators

UpdatedMay 15, 2025
Python

SciML /Optimization.jl

Sponsor

Star806

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 derivative-free-optimization sciml local-optimization

UpdatedNov 4, 2025
Julia

MilesCranmer /SymbolicRegression.jl

Star744

Distributed High-Performance Symbolic Regression in Julia

distributed-systems data-science machine-learning julia genetic-algorithm symbolic symbolic-regression evolutionary-algorithms symbolic-computation automl interpretable-ml explainable-ai sciml equation-discovery

UpdatedOct 27, 2025
Julia

SciML /SciMLTutorials.jl

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Star736

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

python r julia ode dde partial-differential-equations differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations hacktoberfest neural-ode scientific-machine-learning neural-differential-equations sciml

UpdatedAug 12, 2025
CSS

benmoseley /harmonic-oscillator-pinn

Star651

Code accompanying my blog post: So, what is a physics-informed neural network?

neural-networks sciml pinns physics-informed-neural-networks physics-informed-ml physics-informed-machine-learning

UpdatedMar 22, 2022
Jupyter Notebook

SciML /OrdinaryDiffEq.jl

Sponsor

Star608

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 sciml

UpdatedOct 29, 2025
Julia

SciML /diffeqpy

Sponsor

Star583

Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

ode dde differential-equations ordinary-differential-equations numba differentialequations sde dae stochastic-differential-equations delay-differential-equations differential-algebraic-equations sdes scientific-machine-learning sciml

UpdatedOct 17, 2025
Python

SciML /Catalyst.jl

Sponsor

Star500

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 gillespie-algorithm systems-biology-simulation rate-laws scientific-machine-learning sciml

UpdatedOct 27, 2025
Julia

SciML /DataDrivenDiffEq.jl

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Star418

Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

julia ode differential-equations scientific-machine-learning sciml

UpdatedOct 6, 2025
Julia

SciML /SciMLSensitivity.jl

Sponsor

Star369

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 differential-equations differentialequations sde dae sensitivity-analysis hacktoberfest adjoint backpropogation neural-ode scientific-machine-learning neural-sde sciml