Learning two-phase microstructure evolution using neural operators and autoencoder architectures

• Published in: npj computational materials 2022-09, Vol.8 (1), p.1-13, Article 190
• Main Authors: Oommen, Vivek, Shukla, Khemraj, Goswami, Somdatta, Dingreville, Rémi, Karniadakis, George Em
• Format: Article
• Language: English
• Subjects: 639/301/1034/1037; 639/766/25; Characterization and Evaluation of Materials; Chemistry and Materials Science; Computational Intelligence; Design optimization; Efficiency; Evolution; Interpolation; Learning; Materials Science; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Microstructure; Ordinary differential equations; Partial differential equations; Solvers; Theoretical
• ISSN: 2057-3960; 2057-3960
• DOI: 10.1038/s41524-022-00876-7

Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost of computationally taxing processes such as in optimization and design of materials. The intrinsic discontinuous nature of the physical phenomena incurred by the presence of sharp phase boundaries makes the training of the surrogate model cumbersome. We develop a framework that integrates a convolutional autoencoder architecture with a deep neural operator (DeepONet) to learn the dynamic evolution of a two-phase mixture and accelerate time-to-solution in predicting the microstructure evolution. We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space. After DeepONet is trained in the latent space, it can be used to replace the high-fidelity phase-field numerical solver in interpolation tasks or to accelerate the numerical solver in extrapolation tasks.