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.

Differentiable SDE solvers with GPU support and efficient sensitivity analysis.

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

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 PyTorch library entirely dedicated to neural differential equations, implicit models and related numerical methods

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

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

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

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

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

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

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)

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

Boundary value problem (BVP) solvers for scientific machine learning (SciML)

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

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

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

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

Neural Laplace: Differentiable Laplace Reconstructions for modelling any time observation with O(1) complexity.

Code for "'Hey, that's not an ODE:' Faster ODE Adjoints via Seminorms" (ICML 2021)