Top 6 Julia ordinary-differential-equation Projects

ModelingToolkit.jl

15 1,333 9.8 Julia

An 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
NeuralPDE.jl

10 901 9.7 Julia

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Project mention: Automatically install huge number of dependency? | /r/Julia | 2023-05-31

The documentation has a manifest associated with it: https://docs.sciml.ai/NeuralPDE/dev/#Reproducibility. Instantiating the manifest will give you all of the exact versions used for the documentation build (https://github.com/SciML/NeuralPDE.jl/blob/gh-pages/v5.7.0/assets/Manifest.toml). You just ]instantiate folder_of_manifest. Or you can use the Project.toml.

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DiffEqFlux.jl

2 837 8.9 Julia

Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
OrdinaryDiffEq.jl

3 498 9.6 Julia

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Project mention: Modern Numerical Solving methods | /r/DifferentialEquations | 2023-07-06

There has been a lot of research in Runge Kutta methods in the last couple decades which resulted in all kind of specialized Runge Kutta methods. You have high order ones, RK methods for stiff problems, embedded RK methods which benefit from adaprive step size control, RK-Nystrom methods for second order Problems, symplectic RK methods which preserve energy (eg. hamiltonian) ando so on. If you are interested in the numerics and the use cases I highly recommend checking out the Julia Libary OrdinaryDiffEq (https://github.com/SciML/OrdinaryDiffEq.jl). If you look into the documentation you find A LOT of implemented RK methods for all kind of use cases.

DiffEqBase.jl

1 295 9.3 Julia

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
ModelingToolkitStandardLibrary.jl

2 98 9.1 Julia

A standard library of components to model the world and beyond

NOTE: The open source projects on this list are ordered by number of github stars. The number of mentions indicates repo mentiontions in the last 12 Months or since we started tracking (Dec 2020).