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.

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

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

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

NeuralNetDiffEq.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.

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

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

Modia.jl298Modeling and simulation of multidomain engineering systems

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.

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.

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

ChaosTools.jl183Tools for the exploration of chaos and nonlinear dynamics

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

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

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.

FunctionalModels.jl111Equationbased modeling and simulations in Julia

ControlSystemIdentification.jl108System Identification toolbox for LTI systems, compatible with ControlSystems.jl

CausalityTools.jl104Algorithms for detecting associations, dynamical influences and causal inference from data.

Causal.jl102Causal.jl  A modeling and simulation framework adopting causal modeling approach.

ProbNumDiffEq.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

ODEFilters.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Mads.jl94MADS: Model Analysis & Decision Support

SymbolicNumericIntegration.jl93SymbolicNumericIntegration.jl: SymbolicNumerics for Solving Integrals

LowLevelParticleFilters.jl90State estimation, smoothing and parameter estimation using Kalman and particle filters.

PowerDynamics.jl88Package for dynamical modeling of power grids

TaylorIntegration.jl84ODE integration using Taylor's method, and more, in Julia

ViscousFlow.jl84A framework for simulating viscous incompressible flows about arbitrary body shapes.

ValidatedNumerics.jl81Rigorous floatingpoint calculations with interval arithmetic in Julia

SemanticModels.jl76A julia package for representing and manipulating model semantics

ModelingToolkitStandardLibrary.jl76A standard library of components to model the world and beyond

EasyModelAnalysis.jl74High level functions for analyzing the output of simulations
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