Popular GitHub Repositories for Differential Equations

Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)

Differentiable SDE solvers with GPU support and efficient sensitivity analysis.

Brian is a free, open source simulator for spiking neural networks.

Code for "Neural Controlled Differential Equations for Irregular Time Series" (Neurips 2020 Spotlight)

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, 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.

Differentiable controlled differential equation solvers for PyTorch with GPU support and memory-efficient adjoint backpropagation.

Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

Solve forward and inverse problems related to partial differential equations using finite basis physics-informed neural networks (FBPINNs)

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

Surrogate modeling and optimization for scientific machine learning (SciML)

18.S096 - Applications of Scientific Machine Learning

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

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

Reservoir computing utilities for scientific machine learning (SciML)

"Graph Neural Controlled Differential Equations for Traffic Forecasting", AAAI 2022

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

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations