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.
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Acknowledgements
Jia Zhao would like to acknowledge the support from NSF DMS-1816783 and NVIDIA Corporation for their donation of a Quadro P6000 GPU for conducting some of the numerical simulations in this paper.
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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
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DOI: https://doi.org/10.1007/s42967-020-00105-2