75 Open Source Ode Software Projects

Code for Tensorflow Machine Learning Cookbook

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components

A 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

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

A collection of resources regarding the interplay between differential equations, deep learning, dynamical systems, control and numerical methods.

Convert julia objects to LaTeX equations, arrays or other environments.

Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

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

High performance differential equation solvers for ordinary differential equations, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software

Julia 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

Java 3D Physics Engine & Library

Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML)

Fortran Object-Oriented Differential-equations Integration Environment, FOODIE

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystem

PyDEns is a framework for solving Ordinary and Partial Differential Equations (ODEs & PDEs) using neural networks

Benchmarks for scientific machine learning (SciML) software and differential equation solvers

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

Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

Simulate from ODE-based population PK/PD and QSP models in R

Code for the paper "Learning Differential Equations that are Easy to Solve"

Reachability and Safety of Nondeterministic Dynamical Systems

Solving linear, nonlinear equations, ordinary differential equations, ... using numerical methods in fortran

Game Engine Framework for the D programming language

A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, and more for ODEs, SDEs, DDEs, DAEs, etc.

Bulirsch-Stoer integration of systems of ordinary differential equations in JavaScript

Mirror of Apache ODE

A collection of numerical methods written in Nim

A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations

Advanced Multilanguage Interface to CVODES and IDAS

A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

Deep Developmental Reinforcement Learning

Build 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)

Validates XML documents with XML Schema and Schematron

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

library of C++ functions that support applications of Stan in Pharmacometrics

Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization

Methods to compute sets of states reachable by dynamical systems

Modern Fortran Edition of Hairer's DOP853 ODE Solver

irrlamb is a 3D game that probably involves a lot of physics and frustrating gameplay.

The SciML Scientific Machine Learning Software Organization Website

Owl's Differential Equation Solvers

Modern Fortran implementation of the DDEABM Adams-Bashforth algorithm

Tutorials on Control Theory

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

Notebooks in support of of the Part IA (Michaelmas Term) mathematics course at the Department of Engineering at University of Cambridge

A simple but powerful C++ DAE (Differential Algebraic Equation) solver

The SBML Test Suite is a conformance testing system. It allows developers and users to test the degree and correctness of the SBML support provided in a software package.

Port-Hamiltonian Approach to Neural Network Training

An ordinary differential equation solving library in golang.

A generic Runge-Kutta module to solve a system of ODEs

Solvers for steady states in scientific machine learning (SciML)

Fortran Library for numerical INTegration of differential equations

A library for solving differential equations using neural networks based on PyTorch, used by multiple research groups around the world, including at Harvard IACS.

C++ library for ODE integration via Taylor's method and LLVM

Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

Python library for ODE integration via Taylor's method and LLVM

Operator Inference for data-driven, non-intrusive model reduction of dynamical systems.

A Python Framework for Modeling and Analysis of Signaling Systems

ODE system solver made simple. For IVPs (initial value problems).

Parameter estimation for dynamical models using high-performance computing, batch and mini-batch optimizers, and dynamic load balancing.

Adaptive solver for stiff systems of ODEs using semi-implicit Runge-Kutta method of third order

SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit

Files for my Nonlinear Systems and Controls class.

A package for the Go programming language to solve ordinary differential equations.

Vehicle dynamics simulator

Tool to convert an ODE model specified in the YAML format to SBML.

ODE system solver using dG(q), time-discontinuous Galerkin with Lobatto basis.

A Python library for solving Initial Value Problems using various numerical integration methods.

A full reconstruction of the paper: A new model for control systems with friction (Canudas de Wit et al., 1995, IEEE Transactions on Automatic Control)

[TGRS21] Crop Classification under Varying Cloud Cover with Neural Ordinary Differential Equations