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DiffEqBase.jl is a component package in the DiffEq ecosystem. It holds the common types and utility functions which are shared by other solver packages to promote code reuse in the differential equation solver code. Users interested in using this functionality in full should check out DifferentialEquations.jl
The documentation for the interfaces here can be found in DiffEqDocs.jl and DiffEqDevDocs.jl.
DifferentialEquations.jl
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
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)ModelingToolkit.jl
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 equationsNeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulationDiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methodsSciMLTutorials.jl
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.Optimization.jl
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.OrdinaryDiffEq.jl
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
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organizationCatalyst.jl
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
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organizationSciMLSensitivity.jl
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.Surrogates.jl
Surrogate modeling and optimization for scientific machine learning (SciML)SciMLBenchmarks.jl
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, RDiffEqOperators.jl
Linear operators for discretizations of differential equations and scientific machine learning (SciML)DiffEqGPU.jl
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystemDiffEqDocs.jl
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystemNeuralOperators.jl
DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in JuliaLinearSolve.jl
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.NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.Integrals.jl
A common interface for quadrature and numerical integration for the SciML scientific machine learning organizationDataInterpolations.jl
A library of data interpolation and smoothing functionsSciMLStyle
A style guide for stylish Julia developersStochasticDiffEq.jl
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystemReservoirComputing.jl
Reservoir computing utilities for scientific machine learning (SciML)Sundials.jl
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 mannerRecursiveArrayTools.jl
Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applicationsMethodOfLines.jl
Automatic Finite Difference PDE solving with Julia SciMLdiffeqr
Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystemJumpProcesses.jl
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)SciMLBase.jl
The Base interface of the SciML ecosystemNBodySimulator.jl
A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamicsColPrac
Contributor's Guide on Collaborative Practices for Community PackagesDiffEqBayes.jl
Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learningLabelledArrays.jl
Arrays which also have a label for each element for easy scientific machine learning (SciML)PolyChaos.jl
A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.SymbolicNumericIntegration.jl
SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving IntegralsModelingToolkitStandardLibrary.jl
A standard library of components to model the world and beyondPreallocationTools.jl
Tools for building non-allocating pre-cached functions in Julia, allowing for GC-free usage of automatic differentiation in complex codesStructuralIdentifiability.jl
Fast and automatic structural identifiability software for ODE systemsODE.jl
Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.QuasiMonteCarlo.jl
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)RuntimeGeneratedFunctions.jl
Functions generated at runtime without world-age issues or overheadFEniCS.jl
A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming languageDiffEqCallbacks.jl
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solversExponentialUtilities.jl
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.EllipsisNotation.jl
Julia-based implementation of ellipsis array indexing notation `..`EasyModelAnalysis.jl
High level functions for analyzing the output of simulationsAutoOptimize.jl
Automatic optimization and parallelization for Scientific Machine Learning (SciML)ParameterizedFunctions.jl
A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applicationsHighDimPDE.jl
A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionalitySciMLExpectations.jl
Fast uncertainty quantification for scientific machine learning (SciML) and differential equationsMultiScaleArrays.jl
A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulationsSimpleNonlinearSolve.jl
Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.DiffEqNoiseProcess.jl
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
CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.SparsityDetection.jl
Automatic detection of sparsity in pure Julia functions for sparsity-enabled scientific machine learning (SciML)DelayDiffEq.jl
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.SciMLDocs
Global documentation for the Julia SciML Scientific Machine Learning OrganizationDiffEqProblemLibrary.jl
A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning toolssciml.ai
The SciML Scientific Machine Learning Software Organization WebsiteDiffEqParamEstim.jl
Easy scientific machine learning (SciML) parameter estimation with pre-built loss functionsStatic.jl
Static types useful for dispatch and generated functions.GlobalSensitivity.jl
Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in JuliaDeepEquilibriumNetworks.jl
Implicit Layer Machine Learning via Deep Equilibrium Networks, O(1) backpropagation with accelerated convergence.MinimallyDisruptiveCurves.jl
Finds relationships between the parameters of a mathematical modelDiffEqPhysics.jl
A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)MuladdMacro.jl
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 ecosystemDiffEqDevTools.jl
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)OperatorLearning.jl
No need to train, he's a smooth operatorBoundaryValueDiffEq.jl
Boundary value problem (BVP) solvers for scientific machine learning (SciML)SciMLOperators.jl
SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in JuliaSBMLToolkit.jl
SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkitHelicopterSciML.jl
Helicopter Scientific Machine Learning (SciML) Challenge ProblemADTypes.jl
Repository for automatic differentiation backend typesRootedTrees.jl
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)SciMLWorkshop.jl
Workshop materials for training in scientific computing and scientific machine learningAutoOffload.jl
Automatic GPU, TPU, FPGA, Xeon Phi, Multithreaded, Distributed, etc. offloading for scientific machine learning (SciML) and differential equationsModelOrderReduction.jl
High-level model-order reduction to automate the acceleration of large-scale simulationsModelingToolkitCourse
A course on composable system modeling, differential-algebraic equations, acausal modeling, compilers for simulation, and building digital twins of real-world devicesDifferenceEquations.jl
Solving difference equations with DifferenceEquations.jl and the SciML ecosystem.DASSL.jl
Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organizationFiniteVolumeMethod.jl
Solver for two-dimensional conservation equations using the finite volume method in Julia.SteadyStateDiffEq.jl
Solvers for steady states in scientific machine learning (SciML)TruncatedStacktraces.jl
Simpler stacktraces for the Julia Programming LanguagePDESystemLibrary.jl
A library of systems of partial differential equations, as defined with ModelingToolkit.jl in JuliaDiffEqOnline
It's Angular2 business in the front, and a Julia party in the back! It's scientific machine learning (SciML) for the webReactionNetworkImporters.jl
Julia Catalyst.jl importers for various reaction network file formats like BioNetGen and stoichiometry matricesStochasticDelayDiffEq.jl
Stochastic delay differential equations (SDDE) solvers for the SciML scientific machine learning ecosystemDiffEqOnlineServer
Backend for DiffEqOnline, a webapp for scientific machine learning (SciML)MathML.jl
Julia MathML parserIRKGaussLegendre.jl
Implicit Runge-Kutta Gauss-Legendre 16th order (Julia)SimpleDiffEq.jl
Simple differential equation solvers in native Julia for scientific machine learning (SciML)DiffEqFinancial.jl
Differential equation problem specifications and scientific machine learning for common financial modelsModelingToolkitNeuralNets.jl
Symbolic-Numeric Universal Differential Equations for Automating Scientific Machine Learning (SciML)SciPyDiffEq.jl
Wrappers for the SciPy differential equation solvers for the SciML Scientific Machine Learning organizationSciMLTutorialsOutput
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.OptimalControl.jl
A component of the SciML scientific machine learning ecosystem for optimal controlMATLABDiffEq.jl
Common interface bindings for the MATLAB ODE solvers via MATLAB.jl for the SciML Scientific Machine Learning ecosystemIfElse.jl
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