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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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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DataDrivenDiffEq.jl372Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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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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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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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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DiffEqBase.jl243The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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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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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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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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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
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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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JumpProcesses.jl109Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)
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DiffEqJump.jl109Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)
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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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ODE.jl101Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.
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