SciML Modeling Libraries

While in theory one can build perfect code for all models from scratch, in practice many scientists and engineers need or want some help! The SciML modeling tools provide a higher level interface over the equation solvers which helps the translation from good models to good simulations in a way that abstracts away the mathematical and computational details without giving up performance.

ModelingToolkit.jl: Acausal Symbolic Modeling

Acausal modeling is an extension of causal modeling that is more composable and allows for more code reuse. Build a model of an electric engine, then build a model of a battery, and now declare connections by stating "the voltage at the engine equals the voltage at the connector of the battery", and generate the composed model. The tool for this is ModelingToolkit.jl. ModelingToolkit.jl is a sophisticated symbolic modeling library which allows for specifying these types of large-scale differential equation models in a simple way, abstracting away the computational details. However, its symbolic analysis allows for generating much more performant code for differential-algebraic equations than most users could ever write by hand, with its structural_simplify automatically correcting the model to improve parallelism, numerical stability, and automatically remove variables which it can show are redundant.

ModelingToolkit.jl is the base of the SciML symbolic modeling ecosystem, defining the AbstractSystem types, such as ODESystem, SDESystem, OptimizationSystem, PDESystem, and more, which are then used by all of the other modeling tools. As such, when using other modeling tools like Catalyst.jl, the reference for all of the things that can be done with the symbolic representation is simply ModelingToolkit.jl.

ModelingToolkitStandardLibrary.jl: A Standard Library for ModelingToolkit

Given the composable nature of acausal modeling systems, it's helpful to not have to define every component from scratch and instead build off a common base of standard components. ModelingToolkitStandardLibrary.jl is that library. It provides components for standard models to start building everything from circuits and engines to robots.

Catalyst.jl: Chemical Reaction Networks (CRN), Systems Biology, and Quantiative Systems Pharmacology (QSP) Modeling

Catalyst.jl is a modeling interface for efficient simulation of chemical master equation representations chemical reaction networks and other systems models. It uses a highly intuitive chemical reaction syntax interface which generates all of the extra functionality necessary for the fastest use with DiffEqJump.jl and DifferentialEquations.jl. Its ReactionSystem type is a programmable extension of the ModelingToolkit AbstractSystem interface, meaning that complex reaction systems can be generated through code.

For an overview of the library, see Modeling Biochemical Systems with Catalyst.jl - Samuel Isaacson

NBodySimulator.jl: A differentiable simulator for N-body problems, including astrophysical and molecular dynamics

NBodySimulator.jl is differentiable simulator for N-body problems, including astrophysical and molecular dynamics. It uses the DifferentialEquations.jl solvers, allowing for one to choose between a large variety of symplectic integration schemes. It implements many of the thermostats required for doing standard molecular dynamics approximations.

ParameterizedFunctions.jl: Simple Differential Equation Definitions Made Easy

This image that went viral is actually runnable code from ParameterizedFunctions.jl. Define equations and models using a very simple high level syntax and let the code generation tools build symbolic fast Jacobian, gradient, etc. functions for you.

Model Import Libraries

SBMLToolkit.jl: SBML Import

SBMLToolkit.jl is a library for reading SBML files into the standard formats for Catalyst.jl and ModelingToolkit.jl. There are more than one thousand biological models available in the the BioModels Repository.

CellMLToolkit.jl: CellML Import

CellMLToolkit.jl is a library for reading CellML files into the standard formats for ModelingToolkit.jl. There are several hundred biological models available in the the CellML Model Repository.

ReactionNetworkImporters.jl: BioNetGen Import

ReactionNetworkImporters.jl is a library for reading BioNetGen files into the standard formats for Catalyst.jl and ModelingToolkit.jl.

Third Party Tools of Note

ReactionMechanismSimulator.jl: Simulation and Analysis of Large Chemical Reaction Systems

ReactionMechanismSimulator.jl is a tool for simulating and analyzing large chemical reaction mechanisms. It interfaces with the ReactionMechanismGenerator suite for automatically constructing reaction pathways from chemical components to quickly build realistic models of chemical systems.

MomentClosure.jl: Automated Generation of Moment Closure Equations

MomentClosure.jl is a library for generating the moment closure equations for a given chemical master equation or stochastic differential equation. Thus instead of solving a stochastic model thousands of times to find the mean and variance, this library can generate the deterministic equations for how the mean and variance evolve in order to be solved in a single run. MomentClosure.jl uses Catalyst ReactionSystem and ModelingToolkit SDESystem types as the input for its symbolic generation processes.

FiniteStateProjection.jl: Direct Solution of Chemical Master Equations

FiniteStateProjection.jl is a library for finite state projection direct solving of the chemical master equation. It automatically converts the Catayst ReactionSystem definitions into ModelingToolkit ODESystem representations for the evolution of probability distributions to allow for directly solving the weak form of the stochastic model.

AlgebraicPetri.jl: Applied Category Theory of Modeling

AlgebraicPetri.jl is a library for automating the intuitive generation of dynamical models using a Category theory based approach.

Agents.jl: Agent-Based Modeling Framework in Julia

If one wants to do agent-based modeling in Julia, Agents.jl is the go-to library. It's fast and flexible, making it a solid foundation for any agent-based model.