Shallow_Water_Equations_NN4PDEs

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Shallow_Water_Equations_NN4PDEs

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This repository contains SWE simulation codes including multi-resolution and parallel codes.

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# Shallow Water Equations Discretisation and Solution using Neural Networks

This repository presents a novel approach to the discretisation and solution of the Shallow Water Equations using finite difference (FD), finite volume (FV), and finite element methods (FE). Our method reformulates the discretised system of equations as a discrete convolution, analogous to a convolutional layer in a neural network, and solves it using Jacobi iteration.

## Abstract
on the finite element (FE) method. The discretisation is expressed as the convolutional layer of a neural network whose weights are determined by integrals of the FE basis functions. The resulting system can be
solved with explicit or implicit methods. Expressing and solving discretised systems with neural networks has several benefits, including platform-agnostic code that can run on CPUs, GPUs as well as the latest processors
optimised for AI workloads; the model is fully differentiable and suitable for performing optimisation tasks such as data assimilation; easy integration with trained neural networks that could represent sub-grid-scale
models, surrogate models or physics-informed approaches; and speeding up the development of models due to the available functionality in machine-learning libraries. In this paper, we investigate explicit and semi-implicit
methods, and FE discretisations of up to quartic-order elements. A variety of examples is used to demonstrate the neural-network–based SWE solver, ranging from idealised problems with analytical solutions to laboratory
experiments, and we finish with a real-world test case based on the 2005 Carlisle flood.

## Key Features:
- **Platform-Agnostic Code**: Runs seamlessly on CPUs, GPUs, and AI-optimized processors.
- **Neural Network Integration**: Easily integrates with trained neural networks for sub-grid-scale models, surrogate models, or physics-informed approaches.
- **Accelerated Development**: Leverages machine-learning libraries to speed up model development.

## Applications:
- **Idealised Problems**: Validated against analytical solutions.
- **Laboratory Experiments**: Tested with controlled experimental data.
- **Real-World Test Case**: Applied to the 2005 Carlisle flood, demonstrating significant potential speed-ups with AI processors.

## Getting Started
To get started with the code, clone this repository using the code at the bottom of this page or click on each file to download them separately or click on the links below:
- [Carlisle Bathymetry](https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs/blob/main/carlisle-5m.dem.raw)
- [Inlet Points](https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs/blob/main/carlisle.bci)
- [Flowrates](https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs/blob/main/flowrates.csv)

Create a folder on your computer using the terminal and navigate to the folder:
```ruby
mkdir Shallow_Water_Equations_NN4PDEs
```
```ruby
cd Shallow_Water_Equations_NN4PDEs
```
Clone the repository in your folder:
```ruby
git clone https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs.git
```
---
### Carlisle 2005 Flood Event Modeled with NN4PDEs
```geojson
{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "id": 1,
      "properties": {
        "ID": 0
      },
      "geometry": {
        "type": "Polygon",
        "coordinates": [
          [
              [-2.886863, 54.910878],
              [-2.959449, 54.910878],
              [-2.959449, 54.883988],
              [-2.886863, 54.883988],
              [-2.886863, 54.910878]
          ]
        ]
      }
    }
  ]
}
```

---
## Repository Structure
```plaintext
. Shallow_Water_Equations_NN4PDEs
├── Demos/                                 # Folder for animation files
│   ├── 68-hours_simulation.mp4            # mp4 format of the 68 h simulation results
│   └── SWE_2_gif.gif                      # gif format of the 68 h simulation results
├── Documents/                             # Model inputs
│   ├── Carlisle.bci                       # A raster file of the domain
│   └── point_readings_paper.csv           # Coordinates of the reading points in the domain
├── Source_code/                           # Python codes for Linea, Quadratic and parallel simulations
│   ├── Linear/                     
│           ├── AI4SWE_Linear.py           # Main code
│           └── SWE_2D_diff_Linear.py      # External library
│   └── Quadratic/                     
│           ├── AI4SWE_quadratic.py        # Main code
│           └── SWE_2D_diff_Q.py           # External library
```
---

https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs/assets/71018515/f44fed0b-9b45-499a-8383-9e65b6193202

## Installation

### Prerequisites

Before proceeding, ensure that you have the following:

- **Python 3.10**: It is recommended to use Python 3.10 for compatibility with the required packages and libraries.

- **Conda (Preferred)**: Although not essential, it is recommended to use [Conda](https://docs.conda.io/projects/conda/en/latest/user-guide/install/index.html) for managing your Python environment and dependencies. Conda simplifies package management and helps avoid conflicts.

- **GPU with CUDA support**: A GPU that supports CUDA and has at least 20GB of VRAM. Ensure that your CUDA drivers are correctly installed and configured.

### Environment Setup

To set up the environment, run:

```bash
conda env create -f environment.yml
```

Alternatively, you can install the required packages using `requirements.txt`:

```bash
pip install -r requirements.txt
```

Usage
Detailed instructions on how to use the code and run simulations can be found in the docs directory.

## License
This project is licensed under the MIT License. See the LICENSE.md file for details.

## Citation
If you use this project or the related paper in your research, please cite it as follows:

### Paper Citation:

```bibtex
@article{chen2025solving,
  title={Solving the discretised shallow water equations using neural networks},
  author={Chen, Boyang and Nadimy, Amin and Heaney, Claire E and Sharifian, Mohammad Kazem and Estrem, Lluis Via and Nicotina, Ludovico and Hilberts, Arno and Pain, Christopher C},
  journal={Advances in Water Resources},
  pages={104903},
  year={2025},
  publisher={Elsevier}
}
```

### GitHub Repository Citation:
To cite this GitHub repository, please use the following `bibtex` entry:

```bibtex
@misc{nadimy2025shallow,
  author = {Amin Nadimy},
  title = {Shallow Water Equations and Neural Networks for Solving PDEs},
  year = {2025},
  url = {https://github.com/Amin-Nadimy/Shallow_Water_Equations_NN4PDEs}
}
```
## Contact and references
For more information please contact me via:
- Email: amin.nadimy19@imperial.ac.uk

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