113 Packages since 2013
User Packages

DifferentialEquations.jl2503Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.

ModelingToolkit.jl1212An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physicsinformed machine learning and automated transformations of differential equations

DiffEqFlux.jl771Universal neural differential equations with O(1) backprop, GPUs, and stiff+nonstiff DE solvers, demonstrating scientific machine learning (SciML) and physicsinformed machine learning methods

NeuralNetDiffEq.jl755PhysicsInformed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

NeuralPDE.jl755PhysicsInformed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

SciMLTutorials.jl694Tutorials for doing scientific machine learning (SciML) and highperformance differential equation solving with open source software.

DiffEqTutorials.jl694Tutorials for doing scientific machine learning (SciML) and highperformance differential equation solving with open source software.

GalacticOptim.jl512Mathematical Optimization in Julia. Local, global, gradientbased and derivativefree. Linear, Quadratic, Convex, MixedInteger, and Nonlinear Optimization in one simple, fast, and differentiable interface.

Optimization.jl512Mathematical Optimization in Julia. Local, global, gradientbased and derivativefree. Linear, Quadratic, Convex, MixedInteger, and Nonlinear Optimization in one simple, fast, and differentiable interface.

OrdinaryDiffEq.jl425High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

DataDrivenDiffEq.jl372Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

DiffEqBiological.jl342Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPUparallelized, and O(1) solvers in open source software

Catalyst.jl342Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPUparallelized, and O(1) solvers in open source software

Surrogates.jl281Surrogate modeling and optimization for scientific machine learning (SciML)

DiffEqOperators.jl279Linear operators for discretizations of differential equations and scientific machine learning (SciML)

SciMLBenchmarks.jl252Benchmarks for scientific machine learning (SciML) software, scientific AI, and (differential) equation solvers

SciMLSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

DiffEqSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

DiffEqBase.jl243The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

DiffEqDocs.jl233Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

DiffEqGPU.jl202GPUacceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

StochasticDiffEq.jl200Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Sundials.jl188Julia 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

LinearSolve.jl178LinearSolve.jl: HighPerformance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

ReservoirComputing.jl172Reservoir computing utilities for scientific machine learning (SciML)

Integrals.jl166A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

RecursiveArrayTools.jl166Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

NeuralOperators.jl151DeepONets, (Fourier) Neural Operators, PhysicsInformed Neural Operators, and more in Julia

MethodOfLines.jl118Automatic Finite Difference PDE solving with Julia SciML

DiffEqBayes.jl117Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning

NBodySimulator.jl115A differentiable simulator for scientific machine learning (SciML) with Nbody problems, including astrophysical and molecular dynamics

NonlinearSolve.jl112Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.

DiffEqJump.jl109Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and statedependent rates and mix with differential equations and scientific machine learning (SciML)

PolyChaos.jl109A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

JumpProcesses.jl109Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and statedependent rates and mix with differential equations and scientific machine learning (SciML)

LabelledArrays.jl107Arrays which also have a label for each element for easy scientific machine learning (SciML)

ODE.jl101Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

SymbolicNumericIntegration.jl93SymbolicNumericIntegration.jl: SymbolicNumerics for Solving Integrals

SciMLBase.jl90The Base interface of the SciML ecosystem

RuntimeGeneratedFunctions.jl86Functions generated at runtime without worldage issues or overhead
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