Dependency Packages
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DifferentialEquations.jl2503Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
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DSGE.jl798Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)
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DiffEqFlux.jl771Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
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NeuralNetDiffEq.jl755Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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NeuralPDE.jl755Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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DynamicalSystems.jl725Award winning software library for nonlinear dynamics and nonlinear timeseries analysis
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DiffEqTutorials.jl694Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
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QuantumOptics.jl459Library for the numerical simulation of closed as well as open quantum systems.
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ControlSystems.jl430A Control Systems Toolbox for Julia
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OrdinaryDiffEq.jl425High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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Modia.jl298Modeling and simulation of multidomain engineering systems
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Surrogates.jl281Surrogate modeling and optimization for scientific machine learning (SciML)
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SciMLSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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DiffEqSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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DiffEqGPU.jl202GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
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StochasticDiffEq.jl200Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
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ChaosTools.jl183Tools for the exploration of chaos and nonlinear dynamics
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LinearSolve.jl178LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.
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ReachabilityAnalysis.jl170Methods to compute sets of states reachable by dynamical systems
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TuringModels.jl153Implementations of the models from the Statistical Rethinking book with Turing.jl
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VoronoiFVM.jl134Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method
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MethodOfLines.jl118Automatic Finite Difference PDE solving with Julia SciML
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NBodySimulator.jl115A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics
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NonlinearSolve.jl112High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
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FunctionalModels.jl111Equation-based modeling and simulations in Julia
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ControlSystemIdentification.jl108System Identification toolbox for LTI systems, compatible with ControlSystems.jl
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CausalityTools.jl104Algorithms for detecting associations, dynamical influences and causal inference from data.
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Causal.jl102Causal.jl - A modeling and simulation framework adopting causal modeling approach.
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ProbNumDiffEq.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
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ODEFilters.jl100Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
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Mads.jl94MADS: Model Analysis & Decision Support
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LowLevelParticleFilters.jl90State estimation, smoothing and parameter estimation using Kalman and particle filters.
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PowerDynamics.jl88Package for dynamical modeling of power grids
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TaylorIntegration.jl84ODE integration using Taylor's method, and more, in Julia
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ViscousFlow.jl84A framework for simulating viscous incompressible flows about arbitrary body shapes.
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ValidatedNumerics.jl81Rigorous floating-point calculations with interval arithmetic in Julia
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SemanticModels.jl76A julia package for representing and manipulating model semantics
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EasyModelAnalysis.jl74High level functions for analyzing the output of simulations
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OrbitalTrajectories.jl74OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.
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RigidBodySim.jl68Simulation and visualization of articulated rigid body systems in Julia
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