SciML/NeuralPDE.jl

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

What it solves

NeuralPDE.jl provides a way to solve partial differential equations (PDEs) using neural networks, offering greater generality than classical numerical methods. It allows users to approximate solutions to complex physical systems described by differential equations without relying on traditional discretization grids.

How it works

The package implements Physics-Informed Neural Networks (PINNs). It uses a high-level symbolic interface to automatically construct loss functions based on the physics of the problem (the PDE, boundary conditions, and domains). These loss functions guide the neural network to find a solution that satisfies the physical laws described by the equations.

Who it’s for

It is designed for researchers and engineers working in scientific machine learning (SciML), specifically those needing to solve ODEs, SDEs, RODEs, and PDEs, including integro-differential equations.

Highlights

  • Broad Equation Support: Solves ODEs, SDEs, RODEs, and PDEs, as well as partial integro-differential equations.
  • Automated Setup: Automatically generates physics-informed loss functions from symbolic definitions.
  • Training Acceleration: Includes advanced techniques like quadrature training strategies, adaptive loss functions, and neural adapters.
  • Ecosystem Compatibility: Works with Flux.jl and Lux.jl for GPU-powered layers and integrates with NeuralOperators.jl for DeepONets and Fourier Neural Operators.
  • Data Integration: Supports mixing physics-informed solving with data fitting for hybrid scientific machine learning.

Related

  • Project
    SciML/DiffEqFlux.jl

    A Julia package that integrates differential equation solvers into neural networks to enable the creation of physically informed scientific machine learning models.

  • Project
    i207M/PINNacle

    A comprehensive benchmark for Physics-Informed Neural Networks (PINNs) that implements multiple variants and a challenging dataset to evaluate their performance in solving partial differential equations.

  • Project
    SciML/DifferentialEquations.jl

    A high-performance numerical solver suite for a wide variety of differential equations, supporting scientific machine learning and GPU acceleration.

  • Project
    lululxvi/deepxde

    A scientific machine learning library for solving differential equations and learning operators using physics-informed neural networks and other advanced AI architectures.

  • Project
    SciML/OrdinaryDiffEq.jl

    A comprehensive library of ordinary differential equation solvers and utilities for the Julia language, providing high-performance numerical integration for scientific computing.