Physics‐informed surrogates for electromagnetic dynamics using Transformers and graph neural networks

Abstract

Abstract A novel use case for two data‐driven models, namely, a Transformer and a convolutional graph neural network (CGNN) is proposed. The authors propose to use these models for emulating the dynamics of electromagnetic (EM) propagation and scattering. The Transformer translates a past sequence into a future sequence by constructing representations from the past and using it to predict the future, taking all of its own previous predictions as input at each step of prediction. The CGNN updates the current state of attribute vectors of each node by passing it information (messages) from all of its neighbouring nodes. We train these models with FDTD simulations of plane waves propagating and scattering from PEC objects. The authors demonstrate that, within the bounds of computational resources, the Transformer can be utilised as a surrogate for EM dynamics, providing 14× speed‐up, while the CGNN can be utilised as a next‐frame predictor, providing 9× speed‐up. When comparing the accuracy of these two models with the authors’ previously developed Encoder‐Recurrent‐Decoder (ERD) model, it is observed that the error for both the Transformer and the CGNN remains within the same bound for the ERD model. To the best of the authors’ knowledge, this work is the first to utilise the Transformer as a surrogate for EM dynamics.

Keywords

• electromagnetic wave propagation
• finite difference time‐domain analysis
• neural nets