Modeling and simulation

General modeling and simulation packages in Julia.

Organizations¶

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.
Electa-Git/FMIExchange.jl : load Model Exchange Functional Mock-up Units (FMUs) and simulate them using the DifferentialEquations.jl package.

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.
jverzani/SymPyPythonCall.jl : Julia interface to SymPy via PythonCall.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¶

Differential equations¶

Wikipedia: Differential equations

bradcarman/ModelingToolkitDesigner.jl : A helper tool for visualizing and editing a ModelingToolkit.jl system connections.
cadCAD-org/CadCAD.jl : Complex Adaptive Dynamics Computer Aided Design (CadCAD) is a language for encoding Generalized Dynamical Systems (GDS) as computer programs. The Julia implementation is based on its Python counterpart.
CedarEDA/DAECompiler.jl : the core compiler engine of the Cedar EDA platform. It provides a domain-agnostic framework for high-performance simulation of Differential Algebraic Equations (DAEs). JuliaCon 2024 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.
JuliaComputing/ModelingToolkitSampledData.jl : A standard library with discrete-time components for ModelingToolkit. It requires JuliaSimCompiler.jl, a proprietary product. JuliaCon 2024 video
JuliaDynamics/ConcurrentSim.jl : A discrete event process oriented simulation framework written in Julia.
JuliaHolomorphic/RiemannHilbert.jl : A Julia package for solving a Riemann–Hilbert problem, a certain type of boundary value problem.
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.
nathanaelbosch/ProbNumDiffEq.jl : Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing. JuliaCon 2024 video
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/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.

CliMA/ClimaCore.jl : Tools for building spatial discretization. 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) discretization.
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.
omlins/ParallelStencil.jl : writing high-level code for parallel high-performance stencil computations that can be deployed on both GPUs and CPUs.
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/MethodOfLines.jl : Automatic Finite Difference PDE solving with Julia.
trixi-framework/Trixi.jl : Adaptive high-order numerical simulations of hyperbolic PDEs in Julia. JuliaCon 2021 video

Universal Differential Equations¶

Jack-H-Buckner/UniversalDiffEq.jl : builds Universal Differential Equations (UDEs) to learn nonlinear dynamics from time series data.
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/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.

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.

Difference Equations¶

Encyclopedia of Mathematic: Difference equation

JuliaDynamics/DynamicalSystems.jl : Julia software library for the exploration of chaos and nonlinear dynamics.

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 network, providing an interface between Graphs.jl and DifferentialEquations.jl.

Utilities¶

bifurcationkit/BifurcationKit.jl : Bifurcation Analysis in Julia.
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. Benchmark results

Parameter estimation¶

MarcusGalea/PhysicsInformedRegression.jl : solving inverse problems (parameter estimation) using physics informed regression. It requires well-defined derivatives. JuliaCon 2024 video
SciML/DiffEqParamEstim.jl : a package for simplified parameter estimation with DifferentialEquations.jl.
SciML/SciMLSensitivity.jl : sensitivity analysis and parameter estimation.

Others¶

madsjulia/Mads.jl : MADS, Model Analysis & Decision Support.
ThummeTo/FMI.jl : integrating the Functional Mock-Up Interface.
OpenModelica/OMJulia.jl : Julia scripting OpenModelica interface.