---
license: apache-2.0
language:
- en
library_name: pytorch
tags:
- OneScience
- computational-fluid-dynamics
- physics-informed-neural-network
- navier-stokes
- hard-boundary-conditions
---
<p align="center">
  <strong>
    <span style="font-size: 30px;">HardBCPINN-SinePipeFlow</span>
  </strong>
</p>

# Model Overview

HardBCPINN-SinePipeFlow is a reproduction of a hard-boundary-condition physics-informed neural network (PINN) for two-dimensional incompressible steady flow in a pipe with sinusoidal walls.

Paper: [Solving Navier-Stokes Equations Using Data-free Physics-Informed Neural Networks With Hard Boundary Conditions](https://arxiv.org/pdf/2511.14497)

# Model Description

HardBCPINN-SinePipeFlow is trained without labeled flow-field data. It takes two-dimensional coordinates `(x, y)` as input and predicts velocity and pressure `(u, v, p)`. The implementation embeds the inlet pressure, outlet pressure, and no-slip wall conditions in an output transformation, so the model satisfies these hard boundary conditions throughout training. The interior flow is optimized using residuals of the incompressible Navier-Stokes equations.

## Use Cases

| Use Case | Description |
| :--- | :--- |
| Internal pipe-flow solution | Solve two-dimensional steady velocity and pressure fields in a pipe with sinusoidal boundaries |
| PINN workflow validation | Validate data-free PINN training with hard boundary constraints |

# 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.
- A CPU can be used for import checks and small-scale pipeline validation, but full training will be slow.
- DCU users must install DTK in advance. DTK 25.04.2 or later, or the OneScience-recommended version for the target cluster, is recommended.

### Download the Model Package from Hugging Face

```bash
pip install -U huggingface_hub
hf download OneScience-Group/HardBCPINN-SinePipeFlow --local-dir ./HardBCPINN-SinePipeFlow
cd HardBCPINN-SinePipeFlow
```

### Set Up the Runtime Environment

**DCU Environment**

```bash
# Activate DTK and Conda first
conda create -n onescience311 python=3.11 -y
conda activate onescience311
# Installation with uv is also supported
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
# Installation with uv is also supported
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
```

### Training Data

This package reproduces the Reynolds-number-100 sinusoidal-wall pipe-flow experiment from Section 3.3 of the paper. It is a data-free PINN task and does not require an external labeled dataset. The script generates collocation points, boundary points, and a visualization grid from the geometry and boundary conditions specified in the paper:

```bash
python scripts/fake_data.py
```

The default geometry parameters are `R0=0.05`, `A=0.005`, `N=6`, and `L=1.0`. The inlet pressure is `0.1`, and the outlet pressure is `0.0`.

### Training

```bash
python scripts/train.py
```

The default training configuration saves the checkpoint to:

```text
./weight/best_model.pth
```

### Model Weights

The `weight/` directory contains a trained checkpoint that can be used directly for inference.

- Weight file: `weight/best_model.pth`
- File size: 340,962 bytes
- SHA256: `f41bf976775dc18af7d01857dc858517c1978de9830c55afd68ccbf9b6cbd030`
- Training length: 300,000 iterations
- Measured metrics: `eval_loss_total=2.567469e-4`, `wall_u_max_abs=0`, and `wall_v_max_abs=0`

Table 7 of the paper reports errors relative to the CFD reference solution at Re=100: `u=0.0016`, `v=0.0811`, and `p=0.0007`. This model package does not include the CFD reference field used by the paper, so it does not recompute relative L2 error; it reports the PDE residual and hard-boundary errors instead.

### Inference

```bash
python scripts/inference.py
```

### Evaluation and Visualization

```bash
python scripts/result.py
```

# 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

- Original paper: [Solving Navier-Stokes Equations Using Data-free Physics-Informed Neural Networks With Hard Boundary Conditions](https://arxiv.org/pdf/2511.14497).
- This repository retains source attribution and is organized for reproducible execution with OneScience and distribution through Hugging Face.