Discovering Phase Field Models from Image Data with the Pseudo-spectral Physics Informed Neural Networks

TL;DR

This paper introduces SPINN, a novel deep learning framework combining physics-informed neural networks and pseudo-spectral methods to efficiently discover phase field models from image data with minimal data and parameters.

Contribution

The paper proposes SPINN, a new pseudo-spectral PINN framework that improves data efficiency, computational speed, and simplicity over traditional PINNs for discovering PDE models from images.

Findings

Requires only two image snapshots for training

Achieves higher computational efficiency

Uses fewer trainable parameters than baseline PINNs

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 (PINN), 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 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. Thus, it significantly simplifies the training process and assures less 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.