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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.

Scimlbook ⭐ 1,722

Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)

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.

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.

Pdebench ⭐ 522

PDEBench: An Extensive Benchmark for Scientific Machine Learning

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)

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

Surrogates.jl ⭐ 302

Surrogate modeling and optimization for scientific machine learning (SciML)

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

Diffeqoperators.jl ⭐ 279

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

18s096sciml ⭐ 268

18.S096 - Applications of Scientific Machine Learning

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

Linearsolve.jl ⭐ 211

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

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

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

Universal_differential_equations ⭐ 187

Repository for the Universal Differential Equations for Scientific Machine Learning paper, describing a computational basis for high performance SciML

Scimlstyle ⭐ 160

A style guide for stylish Julia developers

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

Arrayinterface.jl ⭐ 130

Designs for new Base array interface primitives, used widely through scientific machine learning (SciML) and other organizations

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)

Diffeqr ⭐ 127

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

Nbodysimulator.jl ⭐ 122

A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics

Latticeqcd.jl ⭐ 120

A native Julia code for lattice QCD with dynamical fermions in 4 dimension.

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

Labelledarrays.jl ⭐ 114

Arrays which also have a label for each element for easy scientific machine learning (SciML)

Scimlbase.jl ⭐ 111

The Base interface of the SciML ecosystem

Kinetic.jl ⭐ 110

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

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

Quasimontecarlo.jl ⭐ 95

Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

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

Parameterizedfunctions.jl ⭐ 75

A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Autooptimize.jl ⭐ 75

Automatic optimization and parallelization for Scientific Machine Learning (SciML)

Multiscalearrays.jl ⭐ 69

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

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

Scimlexpectations.jl ⭐ 61

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

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)

Chemical Reaction Neural Network

Simplenonlinearsolve.jl ⭐ 57

Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.

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.

Sparsitydetection.jl ⭐ 53

Automatic detection of sparsity in pure Julia functions for sparsity-enabled scientific machine learning (SciML)

Worlddynamics.jl ⭐ 53

An open-source framework written in Julia for global integrated assessment models.

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

Sophon.jl ⭐ 50

Efficient, Accurate, and Streamlined Training of Physics-Informed Neural Networks

Odinn.jl ⭐ 49

Global glacier model using Universal Differential Equations for climate-glacier interactions

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

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

Boundaryvaluediffeq.jl ⭐ 39

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

Arrhenius.jl ⭐ 39

Differentiable Reacting Flow Modeling Software

Helicoptersciml.jl ⭐ 37

Helicopter Scientific Machine Learning (SciML) Challenge Problem

Rootedtrees.jl ⭐ 36

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

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

Latentdiffeq.jl ⭐ 33

Latent Differential Equations models in Julia.

Dassl.jl ⭐ 31

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

Modelorderreduction.jl ⭐ 30

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

Mljc Unito Projectx 2020 Public ⭐ 29

Public repository for the proposal “Physics-Informed Machine Learning Simulator for Wildfire Propagation” - MLJC University of Turin - ProjectX2020 Competition (UofT AI)

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

Steadystatediffeq.jl ⭐ 25

Solvers for steady states in scientific machine learning (SciML)

Regneuralde.jl ⭐ 25

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

Diffeqfinancial.jl ⭐ 23

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

Diffeqonlineserver ⭐ 22

Backend for DiffEqOnline, a webapp for scientific machine learning (SciML)

Modelingtoolkitcourse ⭐ 22

A course on composable system modeling, differential-algebraic equations, acausal modeling, compilers for simulation, and building digital twins of real-world devices

Stochasticdelaydiffeq.jl ⭐ 22

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

Matlabdiffeq.jl ⭐ 21

Common interface bindings for the MATLAB ODE solvers via MATLAB.jl 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

Scimltutorialsoutput ⭐ 18

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

Sa Pinns ⭐ 17

Implementation of the paper "Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism" [AAAI-MLPS 2021]

Poissonrandom.jl ⭐ 15

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

Awesome Scientific Machine Learning ⭐ 15

A curated list of awesome Scientific Machine Learning (SciML) papers, resources and software

Tensorflowdiffeq.jl ⭐ 14

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

Commonsolve.jl ⭐ 14

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

Scimlbenchmarksoutput ⭐ 13

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

Daskr.jl ⭐ 12

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

Dimensionalplotrecipes.jl ⭐ 12

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

Diffeqmontecarlo.jl ⭐ 10

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

Diffeqapproxfun.jl ⭐ 10

The tools for proper interactions between ApproxFun.jl and DifferentialEquations.jl for pseudospectiral partial differential equation discretizations in scientific machine learning (SciML)

Odeinterfacediffeq.jl ⭐ 9

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

Desolvediffeq.jl ⭐ 9

Wrappers for calling the R deSolve differential equation solvers from Julia for scientific machine learning (SciML)

Related Searches

Scientific Machine Learning Sciml (84)

Julia Sciml (75)

Differential Equations Sciml (63)

Scientific Sciml (37)

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