Modeling and simulation

General modeling and simulation packages in Julia.

Organizations

• ModiaSim
• SciML
• Julia Dynamics

Resources

• Workshop for ModelingToolkit.jl : A Youtube video for JuliaCon 2021.
• SciML/SciMLTutorials.jl : Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

Loading model files

• LCSB-BioCore/SBML.jl : Julia interface to the Systems Biology Markup Language (SBML) library.
• SciML/CellMLToolkit.jl : a Julia library that connects CellML models to the Scientific Julia ecosystem.
• SciML/ReactionNetworkImporters.jl : Loading BioNetGen .net file.
• SciML/SBMLToolkit.jl : importing models specified in the Systems Biology Markup Language (SBML) into the Julia SciML ecosystem.

Symbolic Computation

Wikipedia: Symbolic Computation

• chakravala/Reduce.jl : Symbolic parser generator for Julia language expressions using REDUCE algebra term rewriter.
• jlapeyre/Symata.jl : language for symbolic mathematics.
• JuliaPy/SymPy.jl : Julia interface to SymPy via PyCall.jl.
• JuliaSymbolics/Symbolics.jl : A fast and modern CAS for a fast and modern language.
• MilesCranmer/SymbolicRegression.jl : Distributed High-Performance symbolic regression in Julia.
• symengine/SymEngine.jl : Julia wrappers of symengine/symengine.

Data structures

See also data-structures.

• jonniedie/ComponentArrays.jl : Arrays with arbitrarily nested named components.
• SciML/LabelledArrays.jl : Arrays with a label for each element.
• SciML/RecursiveArrayTools.jl : Tools for easily handling nestings array objects like arrays of arrays.

Differential equations

Wikipedia: Differential equations

• BenLauwens/SimJulia.jl : A discrete event process oriented simulation framework written in Julia.
• bradcarman/ModelingToolkitDesigner.jl : A helper tool for visualizing and editing a ModelingToolkit.jl system connections.
• DrugowitschLab/DiffModels.jl : Diffusion Model simulation and first-passage time densities in Julia.
• gabrevaya/LatentDiffEq.jl : A high-level Flux + DiffEq library solving Generative ODE modeling with Known Unknowns (GOKU). JuliaCon 2021 video
• jangevaare/Pathogen.jl : Utilities to simulate and perform inference of disease dynamics.
• JuliaApproximation/SingularIntegralEquations.jl : An experimental Julia package for solving singular integral equations.
• JuliaDynamics/DynamicalSystems.jl : Julia software library for the exploration of chaos and nonlinear dynamics.
• JuliaHolomorphic/RiemannHilbert.jl : A Julia package for solving Riemann–Hilbert problems.
• JuliaTurkuDataScience/FdeSolver.jl : A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.
• ModiaSim/Modia.jl : Modia is a Julia package for modeling and simulation of multidomain engineering systems described by differential equations, algebraic equations, and (space-discretized) partial differential equations.
• QuantumBFS/QuDiffEq.jl : Quantum Algorithms for solving differential equations
• SciML/Catalyst.jl : Domain-specific language (DSL) for chemical reaction networks.
• SciML/DataDrivenDiffEq.jl : Data driven modeling and automated discovery of dynamical systems.
• SciML/DiffEqFlux.jl : Combining DifferentialEquations.jl and Flux.jl as its building blocks to support research in Scientific Machine Learning, specifically neural differential equations and universal differential equations.
• SciML/DifferentialEquations.jl : High-performance solvers of differential equations.
• SciML/ModelingToolkit.jl : A modeling framework for automatically parallelized scientific machine learning (SciML) in Julia.
• SciML/SciMLSensitivity.jl : A component of the DiffEq ecosystem for sensitivity analysis.
• SciML/Sundials.jl : A Julia package that interfaces to the Sundials library and includes a nonlinear solver (KINSOL), ODE's (CVODE), and DAE's (IDA).

Partial Differential Equations

• Wikipedia: Finite difference method
• Wikipedia: Finite element method

• Wikipedia: Finite volume method

• PtFEM/PtFEM.jl : Book "Programming the Finite Element Method" by I M Smith, D V Griffiths and L Margetts.

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• CliMA/ClimaCore.jl : Tools for building spatial discretizations. JuliaCon 2021 video
• cvdlab/LinearAlgebraicRepresentation.jl : Official Julia implementation of LAR, the Linear Algebraic Representation for Solid Modeling. LAR is a general representation scheme for geometric and topological modeling.
• FourierFlows/FourierFlows.jl : Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains.
• gridap/Gridap.jl : Grid-based approximation of PDEs with finite element (FE) discretizations.
• j-fu/VoronoiFVM.jl : Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method.
• JuliaFEM/FEMBasis.jl : Package contains interpolation routines for standard finite element function spaces.
• JuliaFEM/JuliaFEM.jl : Finite Element method solver.
• JuliaParallel/PETSc.jl : A Julia interface for PETSc.
• JuliaSmoothOptimizers/Krylov.jl : A Julia Basket of Hand-Picked Krylov Methods.
• lcw/Heptapus.jl : The roofline function is a translation of the roofline code, Accelerated finite element flow solvers.
• PetrKryslUCSD/FinEtools.jl : FinEtools is a package for basic operations on finite element meshes: Construction, modification, selection, and evaluation of quantities defined on a mesh.
• SciML/DiffEqOperators.jl : Linear operators for discretizations of differential equations.
• SciML/MethodOfLines.jl : Automatic Finite Difference PDE solving with Julia.
• SciML/NeuralOperators.jl : Learning the solution operator for partial differential equations in pure Julia.
• SciML/NeuralPDE.jl : Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations.
• trixi-framework/Trixi.jl : Adaptive high-order numerical simulations of hyperbolic PDEs in Julia. JuliaCon 2021 video

Stochastic algorithms

Wikipedia: Stochastic simulation algorithms (SSA) are also included in the DifferentialEquations ecosystem.

• alanderos91/BioSimulator.jl : A stochastic simulation framework in Julia.
• SciML/StochasticDiffEq.jl : Solvers for stochastic differential equations in the SciML ecosystem.
• sdwfrost/Gillespie.jl : Stochastic Gillespie-type simulations using Julia.

Agent-based models

Wikipedia: Agent-based model

• JuliaDynamics/Agents.jl : Agent-based modeling framework in Julia.
• JuliaDynamics/DynamicalBilliards.jl : An easy-to-use, modular and extendable Julia package for Dynamical Billiard systems in two dimensions.
• s-fuerst/Vahana.jl : A framework (not only) for large-scale agent-based models.

Network modeling

• mehalter/Petri.jl : Petri net modeling framework.
• PIK-ICoNe/NetworkDynamics.jl : A package for working with dynamical systems on complex networks. NetworkDynamics.jl provides an interface between Graphs.jl and DifferentialEquations.jl.

Utilities

• JinraeKim/SimulationLogger.jl : providing convenient logging tools for DifferentialEquations.jl.
• jonniedie/SimulationLogs.jl : Signal logging and scoping for DifferentialEquations.jl simulations.
• JuliaDynamics/DrWatson.jl : dealing with simulations and simulation parameters.
• SciML/DataInterpolations.jl : Data interpolation and smoothing functions.
• SciML/SciMLBenchmarks.jl : Benchmarks for scientific machine learning (SciML) software and differential equation solvers.

Others

• madsjulia/Mads.jl : MADS, Model Analysis & Decision Support.