关键词: Phase feld, Linear scheme, Cahn-Hilliard equation, Physics informed neural network

Abstract: In this paper, we introduce a new deep learning framework for discovering the phase-feld models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINNs) and the computational efciency 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 efcient, as the pseudo-spectral method is used for spatial discretization. Thirdly, it requires less trainable parameters compared with the baseline PINN, which signifcantly simplifes the training process and potentially assures fewer local minima or saddle points. We illustrate the efectiveness 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.

Key words: Phase feld, Linear scheme, Cahn-Hilliard equation, Physics informed neural network