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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.

Pdebench ⭐ 522

PDEBench: An Extensive Benchmark for Scientific Machine Learning

Datadrivendiffeq.jl ⭐ 393

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

Surrogates.jl ⭐ 302

Surrogate modeling and optimization for scientific machine learning (SciML)

Diffeqbase.jl ⭐ 282

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

18s096sciml ⭐ 268

18.S096 - Applications of Scientific Machine Learning

Diffeqdocs.jl ⭐ 251

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

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

Kinetic.jl ⭐ 110

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

Fenics.jl ⭐ 86

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

Autooptimize.jl ⭐ 75

Automatic optimization and parallelization for Scientific Machine Learning (SciML)

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)

Cellmltoolkit.jl ⭐ 53

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

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.

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)

Diffeqdevtools.jl ⭐ 46

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

Muladdmacro.jl ⭐ 45

This package contains a macro for converting expressions to use muladd calls and fused-multiply-add (FMA) operations for high-performance in the SciML scientific machine learning ecosystem

Boundaryvaluediffeq.jl ⭐ 39

Boundary value problem (BVP) solvers for scientific machine learning (SciML)

Steadystatediffeq.jl ⭐ 25

Solvers for steady states in scientific machine learning (SciML)

Diffeqfinancial.jl ⭐ 23

Differential equation problem specifications and scientific machine learning for common financial models

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)

Poissonrandom.jl ⭐ 15

Fast Poisson Random Numbers in pure Julia for scientific machine learning (SciML)

Commonsolve.jl ⭐ 14

A common solve function for scientific machine learning (SciML) and beyond

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

Diffeqmontecarlo.jl ⭐ 10

Monte Carlo simulation routines for high-performance parallelization of differential equation solvers and scientific machine learning

Geometricintegratorsdiffeq.jl ⭐ 9

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

Odeinterfacediffeq.jl ⭐ 9

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

Diffeqdevdocs.jl ⭐ 8

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

Resettablestacks.jl ⭐ 7

A stack implementation with a reset! function which avoids garbage collection for scientific machine learning (SciML)

Finiteelementdiffeq.jl ⭐ 5

Solvers for finite element discretizations of PDEs in the SciML scientific machine learning ecosystem

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