gPINNs
Model Overview
gPINNs (Gradient-enhanced Physics-Informed Neural Networks) augment the PDE residual constraints of conventional PINNs with constraints on residual gradients with respect to the input coordinates. This additional higher-order derivative information can improve sample efficiency and solution accuracy for selected forward and inverse problems.
This model package provides one-dimensional and two-dimensional Poisson examples, together with a Burgers equation example using residual-based adaptive refinement (RAR).
Paper: Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
https://doi.org/10.1016/j.cma.2022.114823
Model Description
gPINNs use automatic differentiation to compute both PDE residuals and their coordinate gradients, incorporating both as training constraints. The two-dimensional Poisson example applies a hard-boundary output transformation, while the Burgers example uses RAR to add collocation points progressively in high-residual regions.
Use Cases
| Use Case | Description |
|---|---|
| One-dimensional Poisson equation | Validate joint training with residual-gradient constraints and boundary loss |
| Two-dimensional Poisson equation | Solve a homogeneous Dirichlet boundary-value problem using a hard-boundary output transformation |
| Burgers equation | Combine higher-order automatic differentiation with RAR in high-residual regions |
| Pipeline validation | Validate training, inference, and plotting with the bundled data and pretrained weights |
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 inference and small-scale pipeline validation, but full training will be slow.
- DCU users must install DTK and a PyTorch environment compatible with the target cluster.
Download the Model Package
modelscope download --model OneScience/gPINNs --local_dir ./gPINNs
cd gPINNs
Set Up the Runtime Environment
DCU Environment
# 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
# 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 one- and two-dimensional Poisson examples construct training and evaluation data from analytical solutions; the Burgers example uses the bundled reference solution data/Burgers.npz. Data and training parameters can be adjusted in conf/config.yaml.
Training
To train all examples:
python scripts/train.py --case all
Alternatively, train an individual example with --case 1d, --case 2d, or --case burgers. The --epochs and --nf options override the defaults for the selected example; --lbfgs-iters applies only to the one-dimensional Poisson case, --rar-rounds controls the number of RAR rounds for the Burgers case, and --quick skips RAR for rapid pipeline validation.
Model Weights
This model package provides pretrained weights for the one-dimensional Poisson, two-dimensional Poisson, and Burgers equation examples in the weight/ directory.
Inference, Evaluation, and Visualization
The model package provides weights for validating all three examples. Run:
python scripts/inference.py --case all
The script reports the relative L2 error for each example and saves prediction visualizations under result/. Use --case to select an individual example. Model, data, and training 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
- Yu, J., Lu, L., Meng, X., and Karniadakis, G. E. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Computer Methods in Applied Mechanics and Engineering, 393, 114823, 2022.
- This model package is released under the Apache-2.0 license and retains attribution to the original paper and data sources.