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.

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

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

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

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

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

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

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

🌊 Numerically solving and backpropagating through the wave equation

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

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

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

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

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

Surrogate modeling and optimization for scientific machine learning (SciML)