FPINNs
Model Overview
In this model package, FPINNs refers to Fuzzy Physics-Informed Neural Networks, not fractional PINNs. The architecture augments a fully connected network with a Gaussian fuzzy-membership branch and fuses neural features with fuzzy-rule features to predict solutions to partial differential equations.
The current example solves the Allen–Cahn equation:
u_t - lambda_1 u_xx + lambda_2 (u^3 - u) = 0
Paper: Deep fuzzy physics-informed neural networks for forward and inverse PDE problems
https://doi.org/10.1016/j.neunet.2024.106750
Model Description
FPINNs are trained jointly on data loss and PDE residuals and support both forward and inverse Allen–Cahn problems. The forward task predicts the spatiotemporal solution for known parameters lambda_1=0.0001 and lambda_2=5.0; the inverse task jointly learns the equation solution and both parameters from observations. The model is trained with Adam by default, with optional L-BFGS refinement.
Use Cases
| Use Case | Description |
|---|---|
| Forward Allen–Cahn problem | Predict the complete spatiotemporal solution using known diffusion and reaction parameters |
| Inverse Allen–Cahn problem | Identify diffusion and reaction parameters from solution observations |
| Fuzzy-feature research | Evaluate the fusion of neural features and Gaussian fuzzy-rule features |
| 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 and full-grid inference.
- A CPU can be used for small-scale pipeline validation.
- DCU users must install DTK and a PyTorch environment compatible with the target cluster.
Download the Model Package
modelscope download --model OneScience/FPINNs --local_dir ./FPINNs
cd FPINNs
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 model package includes the Allen–Cahn data file data/AC.mat, which contains spatial coordinates, temporal coordinates, and the corresponding equation solution. The number of training samples and evaluation batch size can be adjusted in conf/config.yaml.
Training
The training task is controlled by common.task in conf/config.yaml: forward selects the forward problem, while inverse selects the inverse problem. After configuring the task, run:
python scripts/train.py
Training checkpoints and histories are saved to the weight/ and result/ directories by default.
Model Weights
This repository provides weights trained on the Allen–Cahn dataset in the weight/ directory.
Inference, Evaluation, and Visualization
After training the selected task, run:
python scripts/inference.py
The inference task is also controlled by common.task. Results are saved as result/fpinn_forward.* or result/fpinn_inverse.* by default. The inverse task additionally reports the recovered lambda_1 and lambda_2 values. Model, training, 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
- Wu, W., Duan, S., Sun, Y., Yu, Y., Liu, D., and Peng, D. Deep fuzzy physics-informed neural networks for forward and inverse PDE problems. Neural Networks, 181, 106750, 2025.
- This model package is released under the Apache-2.0 license and retains attribution to the original paper and data sources.