Fourier neural operator for flow and heat field reconstruction

This is the implementation of ‘’RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator“

• The pipeline of the proposed RecFNO. The RecFNO architecture is composed of an embedding module and multiple Fourier layers.

• Illustrations of four datasets used in this paper. The datasets consists of 2D cylinder wake, 2D steady-state darcy flow, sea surface temperature, and 2D steady-state heat conduction.

• Visualization of reconstructed vorticity and absolute reconstruction error from 2 observations on cylinder wake dataset.

• Visualization of reconstructed temperature field and absolute reconstruction error from 25 observations on heat conduction dataset. The black dots on the last image represent locations of sensor.

• Illustrations of zero-shot super-resolution reconstruction on heat conduction dataset.

• Visualization of the results using noisy snapshots. The noise level is 10 SNR.

Usage

Environment

torch=1.12.1+cu113
torchvision=0.13.1+cu113
tensorboard
scipy
h5py

Data Preparation

Please download the dataset to your local drive, and modify the path of dataset in the $dataset.py$.

• 2D Cylinder Wake.
• 2D Steady-state Darcy Flow.
• Sea Surface Temperature Dataset.
• 2D Steady-state Heat Conduction.

Train and Test

Enter the folder of the corresponding dataset, and run the code with python.

Reference

The project is built upon Fourier neural operator and Voronoi-CNN.

• neuraloperator: https://github.com/neuraloperator/neuraloperator
• Voronoi-CNN: https://github.com/kfukami/Voronoi-CNN

Thank for their excellent works.

Citation

If you find our codes or models useful, please consider to give us a star or cite with:

@misc{https://doi.org/10.48550/arxiv.2302.09808,
  doi = {10.48550/ARXIV.2302.09808},
  url = {https://arxiv.org/abs/2302.09808},
  author = {Zhao, Xiaoyu and Chen, Xiaoqian and Gong, Zhiqiang and Zhou, Weien and Yao, Wen and Zhang, Yunyang},
  title = {RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator}, 
  publisher = {arXiv},
  year = {2023},
  copyright = {arXiv.org perpetual, non-exclusive license}
}