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OneScience-Group/
XPINNs

Name: XPINNs
Rating: 2.5 (17 reviews)

OneScience

XPINNs

physics-informed-neural-networks

domain-decomposition

partial-differential-equations

Poisson

apache-2.0

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XPINNs

Model Overview

XPINNs (Extended Physics-Informed Neural Networks) decompose a complex computational domain into multiple subdomains and assign an independent neural network to each. In addition to enforcing PDE residuals and external boundary conditions, training constrains solution continuity and residual consistency across subdomain interfaces.

This model package reproduces the two-dimensional Poisson benchmark from the XPINNs paper. An irregular X-shaped domain is decomposed into three subdomains governed by:

u_xx + u_yy = exp(x) + exp(y)

Paper: Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
https://doi.org/10.4208/cicp.OA-2020-0164

Model Description

XPINNs assign a separate neural network to each of the three subdomains, using tanh, sin, and cos activation functions by default. The model solves the equation on the irregular domain by jointly optimizing boundary loss, PDE residual loss, interface-value loss, and interface-residual loss.

Use Cases

Use Case	Description
PDE solving on complex domains	Solve a two-dimensional Poisson equation on an irregular X-shaped domain
Domain-decomposition research	Configure independent network architectures and activation functions for different subdomains
Interface-constraint research	Compare losses for interface solution continuity and residual consistency
Pipeline validation	Validate training and inference using the bundled data and a small-scale configuration

Usage

1. OneCode

Use the online OneCode environment for an intelligent, one-click AI for Science (AI4S) programming experience:

Launch OneCode for one-click AI4S programming

2. Manual Setup

Hardware Requirements

A GPU or DCU is recommended for training.
A CPU can be used for small-scale pipeline validation, but training with the full sample set will be slow.
DCU users must install DTK and a PyTorch environment compatible with the target cluster.

Download the Model Package

bash

hf download OneScience-Group/XPINNs --local-dir ./XPINNs
cd XPINNs

Set Up the Runtime Environment

DCU Environment

bash

# Activate DTK and Conda first
conda create -n onescience311 python=3.11 -y
conda activate onescience311
pip install onescience[cfd-dcu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

GPU Environment

bash

# Activate Conda first
conda create -n onescience311 python=3.11 -y libstdcxx-ng=12 libgcc-ng=12 gcc_linux-64=12 gxx_linux-64=12
conda activate onescience311
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

Training Data

The model package includes the two-dimensional Poisson data file data/XPINN_2D_PoissonEqn.mat, which contains interior, boundary, and interface points for the three subdomains together with the exact solution. The number of training samples of each type can be adjusted in conf/config.yaml.

Training

python scripts/train.py

The default weights are saved to weight/xpinn_poisson_2d.pt.

Model Weights

This repository provides weights trained on the two-dimensional Poisson dataset in the weight/ directory.

Inference, Evaluation, and Visualization

After training, run:

python scripts/inference.py

The script reports the overall relative L2 error and saves plots of the exact solution, prediction, and absolute error to result/xpinn_poisson_2d.png. Model, data, loss, and inference parameters can all be modified in conf/config.yaml.

Official OneScience Resources

Platform	OneScience Repository	Skills Repository
Gitee	https://gitee.com/onescience-ai/onescience	https://gitee.com/onescience-ai/oneskills
GitHub	https://github.com/onescience-ai/OneScience	https://github.com/onescience-ai/oneskills

Citations and License

Jagtap, A. D., Kharazmi, E., and Karniadakis, G. E. Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations. Communications in Computational Physics, 28(5), 2002-2041, 2020.
This model package is released under the Apache-2.0 license and retains attribution to the original paper and data sources.