README.md

---
frameworks:
  - pytorch
language:
  - en
license: apache-2.0
tags:
  - OneScience
  - FPINNs
  - fuzzy-physics-informed-neural-networks
  - Allen-Cahn
  - forward-problem
  - inverse-problem
tasks:
  - pde-solving
---
<p align="center">
  <strong>
    <span style="font-size: 30px;">FPINNs</span>
  </strong>
</p>

# 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:

```text
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](https://web-2069360198568017922-iaaj.ksai.scnet.cn:58043/home)

## 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

```bash
modelscope download --model OneScience/FPINNs --local_dir ./FPINNs
cd FPINNs
```

### 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 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:

```bash
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:

```bash
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.