Source code for the Processing Core and Development Environment (PDE)

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.

A library for scientific machine learning and physics-informed learning

Learning in infinite dimension with neural operators.

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) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

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

Simple finite element assemblers

Python package for numerical derivatives and partial differential equations in any number of dimensions.

Source code for APDE: Create and run Processing sketches on an Android device.

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

A framework for hydrodynamics explorations and prototyping

FEATool - "Physics Simulation Made Easy" (Fully Integrated FEA, FEniCS, OpenFOAM, SU2 Solver GUI & Multi-Physics Simulation Platform)

Benchmarks for scientific machine learning (SciML) software, scientific AI, and (differential) equation solvers

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

A Julia package to perform Bifurcation Analysis

Castro (Compressible Astrophysics): An adaptive mesh, astrophysical compressible (radiation-, magneto-) hydrodynamics simulation code for massively parallel CPU and GPU architectures.

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

BOUT++: Plasma fluid finite-difference simulation code in curvilinear coordinate systems

PyClaw is a Python-based interface to the algorithms of Clawpack and SharpClaw. It also contains the PetClaw package, which adds parallelism through PETSc.