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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.

Modelingtoolkit.jl ⭐ 1,292

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

Scimltutorials.jl ⭐ 698

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

Diffeqpy ⭐ 456

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

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.

Scimlsensitivity.jl ⭐ 291

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.

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

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

Diffeqr ⭐ 127

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

Jumpprocesses.jl ⭐ 127

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)

Diffeqbayes.jl ⭐ 119

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

Scimlbase.jl ⭐ 111

The Base interface of the SciML ecosystem

Modelingtoolkitstandardlibrary.jl ⭐ 89

A standard library of components to model the world and beyond

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

Diffeqparamestim.jl ⭐ 60

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

Numerical Methods Fortran ⭐ 54

Solving linear, nonlinear equations, ordinary differential equations, ... using numerical methods in fortran

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

Diffeqdevtools.jl ⭐ 46

Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

Scimlworkshop.jl ⭐ 34

Workshop materials for training in scientific computing and scientific machine learning

Steadystatediffeq.jl ⭐ 25

Solvers for steady states in scientific machine learning (SciML)

A simulator for biological and physiological models

Bridgediffeq.jl ⭐ 5

A thin wrapper over Bridge.jl for the SciML scientific machine learning common interface, enabling new methods for neural stochastic differential equations (neural SDEs)

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