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)

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

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

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.

Physics-Informed Neural networks for Advanced modeling

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

🌊 Numerically solving and backpropagating through the wave equation

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

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

V library to develop Artificial Intelligence and High-Performance Scientific Computations

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)

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

Arrays with arbitrarily nested named components.

Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

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

Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

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

scikit-fmm is a Python extension module which implements the fast marching method.