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.

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

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

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

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.

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

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

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

Arrays with arbitrarily nested named components.

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

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

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

The Base interface of the SciML ecosystem

Advanced Multilanguage Interface to CVODES and IDAS

Fast and automatic structural identifiability software for ODE systems

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

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

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