Derivative-informed Graph Convolutional Autoencoder with Phase Classification for the Lifshitz-Petrich Model
This work addresses the problem of analyzing quasicrystals and multiphase structures in materials science, representing an incremental advancement by applying a novel hybrid method to a classical model.
The authors tackled the challenge of solving and classifying complex spatial patterns in the Lifshitz-Petrich model by proposing a Derivative-informed Graph Convolutional Autoencoder (DiGCA) phase classifier, which accurately classifies solutions and generates phase diagrams with significant improvements in efficiency and accuracy over traditional methods.
The Lifshitz-Petrich (LP) model is a classical model for describing complex spatial patterns such as quasicrystals and multiphase structures. Solving and classifying the solutions of the LP model is challenging due to the presence of high-order gradient terms and the long-range orientational order characteristic of the quasicrystals. To address these challenges, we propose a Derivative-informed Graph Convolutional Autoencoder (DiGCA) to classify the multi-component multi-state solutions of the LP model. The classifier consists of two stages. In the offline stage, the DiGCA phase classifier innovatively incorporates both solutions and their derivatives for training a graph convolutional autoencoder which effectively captures intricate spatial dependencies while significantly reducing the dimensionality of the solution space. In the online phase, the framework employs a neural network classifier to efficiently categorize encoded solutions into distinct phase diagrams. The numerical results demonstrate that the DiGCA phase classifier accurately solves the LP model, classifies its solutions, and rapidly generates detailed phase diagrams in a robust manner, offering significant improvements in both efficiency and accuracy over traditional methods.