Design of a Novel Explainable Adversarial Autoencoder Model for the Electromagnetic Analysis of Functional Materials Based on Physics-Informed Learning

Machine learning models have found their applications in solving problems that can traditionally handle ordinary or partial differential equations. The full-wave simulations solve such equations for functional materials in the microwave regime. These simulations heavily rely on the electrical properties of the materials in predicting microwave characteristics. Currently, most researchers are searching for novel materials and their electrical properties using trial and error methods, for example, microwave absorbing materials, which are used in various civil and military applications. To replace this trial and error method, there is a crucial need for an intelligent system to assist material scientists in fabricating and testing functional materials. This paper proposes a modified Physics-Informed Neural Network (PINN) learning model using an autoencoder with Generative Adversarial Networks (AGAN) and SHapley Additive exPlanations (SHAP) model to assist the researchers in modeling and characterizing any electromagnetic material depending on the user-defined application in a scientifically learned manner with minimum trial and error in selecting the electrical properties of the material. The proposed eXaplainable autoencoder PINN (XA-PINN) algorithm provides a deeper understanding of the decision-making process of microwave absorption frequency bandwidth classification. A proof of concept is demonstrated for dielectric materials by training the model over frequencies from 0.5 to 18 GHz with different permittivity and permeability values. A custom loss is introduced in the proposed XA-PINN model based on the solution of the Riccati equation and mean squared error (MSE).