PeRCNN

Physics-embedded recurrent convolutional neural network

Paper link: [ArXiv] (We will update the final version later...)

By Chengping Rao, Pu Ren, Yang Liu, Hao Sun

Highlights

• Propose a physics-embedded recurrent-convolutional neural network (PeRCNN), which forcibly embeds the physics structure to facilitate learning for data-driven modeling of nonlinear systems
• The physics-embedding mechanism guarantees the model to rigorously obey the given physics based on our prior knowledge
• Present the recurrent π-Block to achieve nonlinear approximation via element-wise product among the feature maps
• Design the spatial information learned by either convolutional or predefined finite-differencebased filters
• Model the temporal evolution with forward Euler time marching scheme

Training and extrapolation results

We show the reconstruction and extrapolation performance of our PeCRNN on 2D Gray-Scott equation below:

Datasets

Due to the file size limit, we attach the google drive [link] to download the datasets.

Models

• PeRCNN model is provided under folders for each dataset
• misc/2d_burgers_ablation contains (part of) models for ablation study
• misc/xx_baselines contains baselines (ConvLSTM, DHPM, ResNet)

Requirements

• pytorch>=1.6 is recommended
• plotly is needed to plot isosurface for 3D case
• TF 1.0 is required for DHPM

Citation

Please consider citing us if you find our research helpful :D

@article{rao2021embedding,
  title={Embedding Physics to Learn Spatiotemporal Dynamics from Sparse Data},
  author={Rao, Chengping and Sun, Hao and Liu, Yang},
  journal={arXiv preprint arXiv:2106.04781},
  year={2021}
}