Discovering Phase Field Models from Image Data with the Pseudo-Spectral Physics Informed Neural Networks
Document Type
Article
Journal/Book Title/Conference
Communications on Applied Mathematics and Computation
Volume
3
Issue
2
Publisher
Springer Singapore
Publication Date
4-2-2021
Award Number
NSF, Division of Mathematical Sciences 1816783
Funder
NSF, Division of Mathematical Sciences
First Page
357
Last Page
369
Abstract
In this paper, we introduce a new deep learning framework for discovering the phase-field models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINNs) and the computational efficiency of the pseudo-spectral methods, which we named pseudo-spectral PINN or SPINN. Unlike the baseline PINN, the pseudo-spectral PINN has several advantages. First of all, it requires less training data. A minimum of two temporal snapshots with uniform spatial resolution would be adequate. Secondly, it is computationally efficient, as the pseudo-spectral method is used for spatial discretization. Thirdly, it requires less trainable parameters compared with the baseline PINN, which significantly simplifies the training process and potentially assures fewer local minima or saddle points. We illustrate the effectiveness of pseudo-spectral PINN through several numerical examples. The newly proposed pseudo-spectral PINN is rather general, and it can be readily applied to discover other PDE-based models from image data.
Recommended Citation
Zhao, J. Discovering Phase Field Models from Image Data with the Pseudo-Spectral Physics Informed Neural Networks. Commun. Appl. Math. Comput. 3, 357–369 (2021). https://doi.org/10.1007/s42967-020-00105-2
