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https://github.com/thu-ml/nuno
[ICML 2023] Non-Uniform Neural Operator (NUNO)
https://github.com/thu-ml/nuno
partial-differential-equations physics point-cloud pytorch simualtion
Last synced: about 1 month ago
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[ICML 2023] Non-Uniform Neural Operator (NUNO)
- Host: GitHub
- URL: https://github.com/thu-ml/nuno
- Owner: thu-ml
- License: mit
- Created: 2023-05-18T11:44:12.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2023-07-03T11:14:03.000Z (over 1 year ago)
- Last Synced: 2024-01-27T20:01:16.611Z (11 months ago)
- Topics: partial-differential-equations, physics, point-cloud, pytorch, simualtion
- Language: Python
- Homepage: https://arxiv.org/abs/2305.18694
- Size: 5.26 MB
- Stars: 13
- Watchers: 6
- Forks: 0
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Non-Uniform Neural Operator (NUNO)
This repository is the official implementation of our [ICML 2023](https://icml.cc/Conferences/2023) paper: [NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data](https://arxiv.org/abs/2305.18694). [Here](assets/slides.pdf) are the corresponding introductory slides.
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such as the FFT. To address this, we introduce the Non-Uniform Neural Operator (NUNO), a comprehensive framework designed for efficient operator learning with non-uniform data. Leveraging a K-D tree-based domain decomposition, we transform non-uniform data into uniform grids while effectively controlling interpolation error, thereby paralleling the speed and accuracy of learning from non-uniform data. We conduct extensive experiments on 2D elasticity, (2+1)D channel flow, and a 3D multi-physics heatsink, which, to our knowledge, marks a novel exploration into **3D PDE problems** with **complex geometries**. Our framework has reduced error rates by up to **60%** and enhanced training speeds by **2x** to **30x**. The code is now available at [this https URL](https://github.com/thu-ml/NUNO).
If you find this work is helpful for your research, please **cite us** with the following BibTeX entry:
```
@article{liu2023nuno,
title={NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data},
author={Liu, Songming and Hao, Zhongkai and Ying, Chengyang and Su, Hang and Cheng, Ze and Zhu, Jun},
journal={arXiv preprint arXiv:2305.18694},
year={2023}
}
```
## Directory Structure
This repository is organized as below:
- `data` (folder for training and testing data)
- `channel` ((2+1)D Channel Flow)
- `elasticity` (2D Elasticity)
- `heatsink` (3D Heatsink)
- `src` (folder for scripts to run experiments)
- `channel` ((2+1)D Channel Flow)
Note: each Python file corresponds to a single baseline method.
- `deeponet.py` (to run DeepONet)
- ...
- `ours_nuunet.py` (to run one of our methods, NU-U-Net)
- `elasticity` (2D Elasticity)
- ...
- `heatsink` (3D Heatsink)
- ...
- `kd_tree` (module of K-D tree algorithm, imported by the above scripts)
- `util` (folder for util functions)
- `assets` (folder for figures and slides)
- `README.md` (this readme)
## Getting Started
1. Install necessary dependencies
Python 3.10.8
```
matplotlib==3.6.2
scikit-learn==1.2.0
torch==1.13.0
tqdm==4.64.1
```
For most experiments, you only need to install the **above four** libraries.
Some (not all) baselines may also require the following libraries:
- `torch-geometric==2.2.0` (visit [this repo](https://github.com/pyg-team/pytorch_geometric) to install the library)
- It is required by GraphNO. If you do no run this baseline, you can ignore this library.
- `sympy==1.11.1`
- It is required by MWNO. If you do no run this baseline, you can ignore this library.
2. Download datasets
For **2D Elasticity**, we refer to [this drive](https://drive.google.com/drive/folders/1cznHmQO-hB_VlWOfh7IFpjsPVOYyghGJ).
Download all the files in folders `Interp`, `Meshes`, `Omesh`, and `Rmesh`. Then put them into the folder `data/elasticity` in *this* repo (**directly move** **`.npy`** **files** but not persevering the original folder structure).
For **(2+1)D Channel Flow** and **3D Heatsink**, we refer to [this drive](https://1drv.ms/u/s!ApNDtoKtGVC6k6AK3AYprkxiZW0qWA?e=7De5vc).
Download all the files in `NUNO/ChannelFlow` and `NUNO/Heatsink`, then put them into `data/channel` and `data/heatsink` in *this* repo, respectively (again, **directly move `.npy` files** but not persevering the original folder structure).
3. Run experiments
```bash
# In the root directory of this repository
# To run baselines for 2D Elasticity
python -m src.elasticity.ours_nufno
# or one of other baselines...
# The file name (in src/elasticity) should be able to represent the baseline method corresponding to the script.
python -m src.elasticity.geofno
# To run scripts in (2+1)D Channel Flow
python -m src.channel.ours_nufno
# or one of other baselines...
# To run scripts in 3D Heatsink
python -m src.heatsink.ours_nufno
# or one of other baselines...
```
## Experimental Results
### 2D Elasticity
### (2+1)D Channel Flow
Note: "oversampling ratio" is a measure for the mesh size.
### 3D Heatsink
