differential-equations

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

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

Linear algebra, eigenvalues, FFT, Bessel, elliptic, orthogonal polys, geometry, NURBS, numerical quadrature, 3D transfinite interpolation, random numbers, Mersenne twister, probability distributions, optimisation, differential equations.

Numerical differential equation solvers in JAX. Autodifferentiable and GPU-capable. https://docs.kidger.site/diffrax/

Differentiable SDE solvers with GPU support and efficient sensitivity analysis.

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

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

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

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

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

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

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)

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

Physics-Informed Neural networks for Advanced modeling

🌊 Numerically solving and backpropagating through the wave equation

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.

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

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