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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ModelingToolkit.jl1212An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
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DSGE.jl798Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)
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Oceananigans.jl781🌊 Julia software for fast, friendly, flexible, ocean-flavored fluid dynamics on CPUs and GPUs
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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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Javis.jl769Julia Animations and Visualizations
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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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NeuralNetDiffEq.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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LoopVectorization.jl659Macro(s) for vectorizing loops.
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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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StaticCompiler.jl395Compiles Julia code to a standalone library (experimental)
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SymbolicRegression.jl377Distributed High-Performance symbolic regression in Julia
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DataDrivenDiffEq.jl372Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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StatisticalRethinking.jl366Julia package with selected functions in the R package `rethinking`. Used in the SR2... projects.
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Trixi.jl363Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia
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DiffEqBiological.jl342Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software
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Catalyst.jl342Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software
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DFTK.jl337Density-functional toolkit
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Modia.jl298Modeling and simulation of multidomain engineering systems
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DiffEqOperators.jl279Linear operators for discretizations of differential equations and scientific machine learning (SciML)
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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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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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DiffEqBase.jl243The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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MonteCarloMeasurements.jl243Propagation of distributions by Monte-Carlo sampling: Real number types with uncertainty represented by samples.
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ComponentArrays.jl231Arrays with arbitrarily nested named components.
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DiffEqGPU.jl202GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
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SparseDiffTools.jl201Fast jacobian computation through sparsity exploitation and matrix coloring
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Octavian.jl201Multi-threaded BLAS-like library that provides pure Julia matrix multiplication
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StochasticDiffEq.jl200Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
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Stan.jl197Stan.jl illustrates the usage of the 'single method' packages, e.g. StanSample, StanOptimize, etc.
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SimpleChains.jl195Simple chains
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Sundials.jl188Julia 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
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ChaosTools.jl183Tools for the exploration of chaos and nonlinear dynamics
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PGFPlots.jl182This library uses the LaTeX package pgfplots to produce plots.
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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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