ICLR2022: Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning
Paper link: [ArXiv]
By Chengping Rao, Pu Ren, Yang Liu, Hao Sun
Three stages of governing equation discovery process
Two types of physics-encoded recurrent network (a. partial physics known; c. physics completely known.)
In Stage-1, we use a physics-encoded recurrent network to reconstruct the high-fidelity data. This step uses the same rountine of https://github.com/Raocp/PeRCNN.
The sparse regression for two equation of u (PDE_FIND_u.py ), v (PDE_FIND_v.py ) is performed separately. We recommend you to run the sparse regression via IPython or Jupyter Notebook.
Based on the result from Stage-2, we perform coefficient finetuning using a physics-based recurrent network (i.e., the recurrent block mimics finite difference discretization of a governing PDE). Note that the finetuning is performed on the orginal sparse data (please refer the paper for explanation).
Set restart=True (it is a bad arg name...) when invoking train() function to read from checkpoint and continue training.