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.

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

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.

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

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.

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.

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

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

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

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

ReachabilityAnalysis.jl189Computing reachable states of dynamical systems in Julia

ChaosTools.jl187Tools for the exploration of chaos and nonlinear dynamics

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

MethodOfLines.jl157Automatic Finite Difference PDE solving with Julia 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)

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)

ControlSystemIdentification.jl132System Identification toolbox, compatible with ControlSystems.jl

NBodySimulator.jl128A differentiable simulator for scientific machine learning (SciML) with Nbody problems, including astrophysical and molecular dynamics

TaylorIntegration.jl127ODE integration using Taylor's method, and more, in Julia

Kinetic.jl122Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

DiffEqBayes.jl121Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning

ODEFilters.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

ProbNumDiffEq.jl118Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

SymbolicNumericIntegration.jl116SymbolicNumericIntegration.jl: SymbolicNumerics for Solving Integrals

Causal.jl115Causal.jl  A modeling and simulation framework adopting causal modeling approach.

LowLevelParticleFilters.jl114State estimation, smoothing and parameter estimation using Kalman and particle filters.
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