Dependency 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.

Turing.jl1807Bayesian inference with probabilistic programming.

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

Symbolics.jl1169A fast and modern CAS for a fast and modern language.

DSGE.jl798Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)

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

DynamicalSystems.jl725Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

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.

QuantumOptics.jl459Library for the numerical simulation of closed as well as open quantum systems.

ControlSystems.jl430A Control Systems Toolbox for Julia

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

Trixi.jl363Trixi.jl: Adaptive highorder numerical simulations of hyperbolic PDEs in Julia

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

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

DFTK.jl337Densityfunctional toolkit

Modia.jl298Modeling and simulation of multidomain engineering systems

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

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

BifurcationKit.jl240A Julia package to perform Bifurcation Analysis

ComponentArrays.jl231Arrays with arbitrarily nested named components.

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

ChaosTools.jl183Tools for the exploration of chaos and nonlinear dynamics

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.

ReachabilityAnalysis.jl170Methods to compute sets of states reachable by dynamical systems

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

TuringModels.jl153Implementations of the models from the Statistical Rethinking book with Turing.jl

TopOpt.jl141A beautifully Julian topology optimization package.

VoronoiFVM.jl134Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method

MethodOfLines.jl118Automatic Finite Difference PDE solving with Julia SciML

PowerSimulationsDynamics.jl118Julia package to run Dynamic Power System simulations. Part of the Scalable Integrated Infrastructure Planning Initiative at the National Renewable Energy Lab.

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
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