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In this paper, we introduce a new deep learning framework for discovering thephase field models from existing image data. The new framework embraces theapproximation power of physics informed neural networks (PINN), and thecomputational efficiency of the pseudo-spectral methods, which we namedpseudo-spectral PINN or SPINN. Unlike the baseline PINN, the pseudo-spectralPINN has several advantages. First of all, it requires less training data. Aminimum of two snapshots with uniform spatial resolution would be adequate.Secondly, it is computationally efficient, as the pseudo-spectral method isused for spatial discretization. Thirdly, it requires less trainable parameterscompared with the baseline PINN. Thus, it significantly simplifies the trainingprocess and assures less local minima or saddle points. We illustrate theeffectiveness of pseudo-spectral PINN through several numerical examples. Thenewly proposed pseudo-spectral PINN is rather general, and it can be readilyapplied to discover other PDE-based models from image data.

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