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Search results for julia differential equations

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103 search results found

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

Diffeqflux.jl ⭐ 810

Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

Scimltutorials.jl ⭐ 698

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

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)

Diffeqgpu.jl ⭐ 261

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

Componentarrays.jl ⭐ 258

Arrays with arbitrarily nested named components.

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

Infiniteopt.jl ⭐ 215

An intuitive modeling interface for infinite-dimensional optimization problems.

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.

Neuraloperators.jl ⭐ 206

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

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)

Reachabilityanalysis.jl ⭐ 184

Compute reachable states of dynamical systems

Nonlinearsolve.jl ⭐ 154

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

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

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

Polychaos.jl ⭐ 112

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

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.

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

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

Structuralidentifiability.jl ⭐ 75

Fast and automatic structural identifiability software for ODE systems

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

Open-source, graph-based Python code generator and analysis toolbox for dynamical systems (pre-implemented and custom models). Most pre-implemented models belong to the family of neural population models.

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)

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

Scientific Programming In Julia ⭐ 60

Repository for B0M36SPJ

Diffeqparamestim.jl ⭐ 60

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

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.

Cellmltoolkit.jl ⭐ 53

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

Sparsitydetection.jl ⭐ 53

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

Diffeqproblemlibrary.jl ⭐ 51

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

Odinn.jl ⭐ 49

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

Petlion.jl ⭐ 48

High-performance simulations of the Porous Electrode Theory for Li-ion batteries

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)

Closedloopreachability.jl ⭐ 42

Reachability analysis for closed-loop control systems

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

Boundaryvaluediffeq.jl ⭐ 39

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

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

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

Reactionnetworkimporters.jl ⭐ 25

Julia Catalyst.jl importers for various reaction network file formats like BioNetGen and stoichiometry matrices

Regneuralde.jl ⭐ 25

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

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)

Manifolddiffeq.jl ⭐ 21

Differential equations on manifolds

Scipydiffeq.jl ⭐ 20

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

Optcontrol.jl ⭐ 20

A tool to solve optimal control problem

Simulationlogs.jl ⭐ 19

Signal logging and scoping for DifferentialEquations.jl simulations.

Piecewisedeterministicmarkovprocesses.jl ⭐ 19

Piecewise Deterministic Markov Processes in Julia

Fenrir.jl ⭐ 18

Physics-Enhanced Regression for Initial Value Problems

Scimltutorialsoutput ⭐ 18

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

Quasinormalmodes.jl ⭐ 18

A Julia package for computing discrete eigenvalues of second order ODEs

Algebraicagents.jl ⭐ 17

A lightweight framework to enable hierarchical, heterogeneous dynamical systems co-integration. Batteries included!

Tensorflowdiffeq.jl ⭐ 14

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

Reactivedynamics.jl ⭐ 14

A Julia package that implements a category of reaction (transportation) network-type dynamical systems.

Flightsims.jl ⭐ 14

A general purpose numerical simulator supporting nested dynamical systems and a convenient macro-based data logger.

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

Double Pendulum Motion Animation ⭐ 12

Animation of the motion a double-pendulum. Both Julia and Python versions of the code are given.

Fdesolver.jl ⭐ 12

FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.

Adapode.jl ⭐ 10

Adaptive P/ODE numerical solvers with Grassmann element TensorField assembly

Geometricintegratorsdiffeq.jl ⭐ 9

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

Exactodereduction.jl ⭐ 9

Exact reduction of ODE models via linear transformations

Inflation.jl ⭐ 9

A Julia package for numerical evaluation of cosmic inflation models. Perturbations are solved for with the transport method. Supports an arbitrary number of fields, arbitrary field space metric, and arbitrary initial conditions.

Odeinterfacediffeq.jl ⭐ 9

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

Simpledifferentialoperators.jl ⭐ 9

Library for simple upwind finite differences

Diffeqdevdocs.jl ⭐ 8

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

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