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Differentialequations.jl ⭐ 2,689

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.

Neuralpde.jl ⭐ 864

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Scimltutorials.jl ⭐ 698

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

Optimization.jl ⭐ 625

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.

Symbolicregression.jl ⭐ 484

Distributed High-Performance Symbolic Regression in Julia

Ordinarydiffeq.jl ⭐ 479

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Catalyst.jl ⭐ 402

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

Diffeqbase.jl ⭐ 282

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Scimlbenchmarks.jl ⭐ 279

Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

Diffeqoperators.jl ⭐ 279

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

Diffeqgpu.jl ⭐ 261

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

Diffeqdocs.jl ⭐ 251

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

Stochasticdiffeq.jl ⭐ 229

Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Reservoircomputing.jl ⭐ 192

Reservoir computing utilities for scientific machine learning (SciML)

Integrals.jl ⭐ 191

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

Recursivearraytools.jl ⭐ 190

Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

Nonlinearsolve.jl ⭐ 154

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

Methodoflines.jl ⭐ 144

Automatic Finite Difference PDE solving with Julia SciML

Diffeqr ⭐ 127

Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystem

Kinetic.jl ⭐ 110

Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

Modelingtoolkitstandardlibrary.jl ⭐ 89

A standard library of components to model the world and beyond

Fenics.jl ⭐ 86

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

Exponentialutilities.jl ⭐ 85

Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form.

Diffeqcallbacks.jl ⭐ 77

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

Multiscalearrays.jl ⭐ 69

A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations

Diffeqnoiseprocess.jl ⭐ 61

A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

Highdimpde.jl ⭐ 61

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

Chemical Reaction Neural Network

Cellmltoolkit.jl ⭐ 53

CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.

Diffeqproblemlibrary.jl ⭐ 51

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

Sciml.ai ⭐ 48

The SciML Scientific Machine Learning Software Organization Website

Diffeqphysics.jl ⭐ 47

A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)

Scimloperators.jl ⭐ 41

SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in Julia

Helicoptersciml.jl ⭐ 37

Helicopter Scientific Machine Learning (SciML) Challenge Problem

Scimlworkshop.jl ⭐ 34

Workshop materials for training in scientific computing and scientific machine learning

Latentdiffeq.jl ⭐ 33

Latent Differential Equations models in Julia.

Modelorderreduction.jl ⭐ 30

High-level model-order reduction to automate the acceleration of large-scale simulations

Autooffload.jl ⭐ 29

Automatic GPU, TPU, FPGA, Xeon Phi, Multithreaded, Distributed, etc. offloading for scientific machine learning (SciML) and differential equations

Diffeqonline ⭐ 26

It's Angular2 business in the front, and a Julia party in the back! It's scientific machine learning (SciML) for the web

Regneuralde.jl ⭐ 25

Official Implementation of "Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics" (ICML 2021)

Stochasticdelaydiffeq.jl ⭐ 22

Stochastic delay differential equations (SDDE) solvers for the SciML scientific machine learning ecosystem

Simplediffeq.jl ⭐ 21

Simple differential equation solvers in native Julia for scientific machine learning (SciML)

Scipydiffeq.jl ⭐ 20

Wrappers for the SciPy differential equation solvers for the SciML Scientific Machine Learning organization

Tensorflowdiffeq.jl ⭐ 14

Using TensorFlow for physics-informed neural networks for scientific machine learning (SciML)

Scimlbenchmarksoutput ⭐ 13

SciML-Bench Benchmarks for Scientific Machine Learning (SciML), Physics-Informed Machine Learning (PIML), and Scientific AI Performance

Dimensionalplotrecipes.jl ⭐ 12

High dimensional numbers and reductions recipes for data visualization of scientific machine learning (SciML)

Daskr.jl ⭐ 12

Interface to DASKR, a differential algebraic system solver for the SciML scientific machine learning ecosystem

Odeinterfacediffeq.jl ⭐ 9

Adds the common API onto ODEInterface classic Fortran methods for the SciML Scientific Machine Learning organization

Geometricintegratorsdiffeq.jl ⭐ 9

Wrappers for GeometricIntegrators.jl into the SciML common interface for scientific machine learning (SciML)

Gaugefields.jl ⭐ 8

Utilities of gauge fields

Diffeqdevdocs.jl ⭐ 8

Developer documentation for the SciML scientific machine learning ecosystem's differential equation solvers

Symbolicindexinginterface.jl ⭐ 8

A general interface for symbolic indexing of SciML objects used in conjunction with Domain-Specific Languages

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