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.

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)

Modia.jl298Modeling and simulation of multidomain engineering systems

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.

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

TopOpt.jl141A beautifully Julian topology optimization package.

Tulip.jl138Interiorpoint solver in pure Julia

NLPModels.jl137Data Structures for Optimization Models

LinearOperators.jl134Linear Operators for Julia

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

MethodOfLines.jl118Automatic Finite Difference PDE solving with Julia SciML

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

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

Nonconvex.jl91Toolbox for nonconvex constrained optimization.

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

PowerDynamics.jl88Package for dynamical modeling of power grids

ImplicitDifferentiation.jl86Automatic differentiation of implicit functions

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

MadNLP.jl84A solver for nonlinear programming

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

ValidatedNumerics.jl81Rigorous floatingpoint calculations with interval arithmetic in Julia

InferOpt.jl78Combinatorial optimization layers for machine learning pipelines
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