Dependency Packages

DifferentialEquations.jl2841Multilanguage 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.jl2026Bayesian inference with probabilistic programming.

ModelingToolkit.jl1410An 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.jl1353Symbolic programming for the next generation of numerical software

NeuralNetDiffEq.jl966PhysicsInformed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

NeuralPDE.jl966PhysicsInformed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

DSGE.jl864Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)

DiffEqFlux.jl861Prebuilt implicit layer architectures with O(1) backprop, GPUs, and stiff+nonstiff DE solvers, demonstrating scientific machine learning (SciML) and physicsinformed machine learning methods

DynamicalSystems.jl834Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

DiffEqTutorials.jl713Tutorials for doing scientific machine learning (SciML) and highperformance differential equation solving with open source software.

GalacticOptim.jl712Mathematical Optimization in Julia. Local, global, gradientbased and derivativefree. Linear, Quadratic, Convex, MixedInteger, and Nonlinear Optimization in one simple, fast, and differentiable interface.

Optimization.jl712Mathematical Optimization in Julia. Local, global, gradientbased and derivativefree. Linear, Quadratic, Convex, MixedInteger, and Nonlinear Optimization in one simple, fast, and differentiable interface.

OrdinaryDiffEq.jl533High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

QuantumOptics.jl528Library for the numerical simulation of closed as well as open quantum systems.

Trixi.jl522Trixi.jl: Adaptive highorder numerical simulations of conservation laws in Julia

ControlSystems.jl508A Control Systems Toolbox for Julia

DiffEqBiological.jl455Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPUparallelized, and O(1) solvers in open source software.

Catalyst.jl455Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPUparallelized, and O(1) solvers in open source software.

DataDrivenDiffEq.jl405Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

SciMLSensitivity.jl329A 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.jl329A 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.

Modia.jl321Modeling and simulation of multidomain engineering systems

DiffEqBase.jl309The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

BifurcationKit.jl301A Julia package to perform Bifurcation Analysis

DiffEqOperators.jl285Linear operators for discretizations of differential equations and scientific machine learning (SciML)

DiffEqGPU.jl283GPUacceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

StochasticDiffEq.jl248Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

LinearSolve.jl244LinearSolve.jl: HighPerformance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

NonlinearSolve.jl227Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.

Integrals.jl225A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

Sundials.jl208Julia 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

VoronoiFVM.jl194Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method

ReachabilityAnalysis.jl189Computing reachable states of dynamical systems in Julia

ChaosTools.jl187Tools for the exploration of chaos and nonlinear dynamics

TopOpt.jl181A package for binary and continuous, single and multimaterial, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.

PowerSimulationsDynamics.jl173Julia package to run Dynamic Power System simulations. Part of the Scalable Integrated Infrastructure Planning Initiative at the National Renewable Energy Lab.

TuringModels.jl163Implementations of the models from the Statistical Rethinking book with Turing.jl

MethodOfLines.jl157Automatic Finite Difference PDE solving with Julia SciML

DiffEqJump.jl139Build 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)

JumpProcesses.jl139Build 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)
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