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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

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.

Latexify.jl ⭐ 501

Convert julia objects to LaTeX equations, arrays or other environments.

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)

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.

Datadrivendiffeq.jl ⭐ 393

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

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

Sundials.jl ⭐ 200

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

Reachabilityanalysis.jl ⭐ 184

Compute reachable states of dynamical systems

Scimlstyle ⭐ 160

A style guide for stylish Julia developers

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

Probnumdiffeq.jl ⭐ 107

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

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

Fractionaldiffeq.jl ⭐ 70

Solve Fractional Differential Equations using high performance numerical methods

Multiscalearrays.jl ⭐ 69

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

Scimlexpectations.jl ⭐ 61

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Diffeqparamestim.jl ⭐ 60

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

Delaydiffeq.jl ⭐ 53

Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.

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

Reachability.jl ⭐ 50

Reachability and Safety of Nondeterministic Dynamical Systems

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)

Diffeqdevtools.jl ⭐ 46

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

Scimloperators.jl ⭐ 41

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

Globalsensitivity.jl ⭐ 41

Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

Fortran Library for numerical INTegration of differential equations

Sbmltoolkit.jl ⭐ 35

SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit

Scimlworkshop.jl ⭐ 34

Workshop materials for training in scientific computing and scientific machine learning

Dassl.jl ⭐ 31

Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization

Steadystatediffeq.jl ⭐ 25

Solvers for steady states in scientific machine learning (SciML)

Scimltutorialsoutput ⭐ 18

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

Fenrir.jl ⭐ 18

Physics-Enhanced Regression for Initial Value Problems

Adapode.jl ⭐ 10

Adaptive P/ODE numerical solvers with Grassmann element TensorField assembly

Exactodereduction.jl ⭐ 9

Exact reduction of ODE models via linear transformations

Chaoticdynamicalsystemlibrary.jl ⭐ 8

A collection of chaotic ODEs.

Sbmlinterface.jl ⭐ 5

Interface between the Systems Biology Markup Language and Julia

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)

Sbml2julia ⭐ 5

A tool to for optimizing parameters of ordinary differential equation (ODE) models. SBML2Julia translates a model from SBML/PEtab format into Julia for Mathematical Programming (JuMP), performs the optimization task and returns the results.

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