Data-driven discovery of thermal illusions through latent-space geometry

TL;DR

This paper introduces a data-driven method using a variational autoencoder to discover thermal illusions and cloaking by analyzing the geometry of high-dimensional thermal data in a latent space, enabling inverse design without complex models.

Contribution

It presents a novel latent-space geometric approach for thermal illusion and cloaking, leveraging deep learning to bypass traditional model constraints.

Findings

Achieved robust thermal illusion and cloaking with positive conductivities.

Demonstrated the method on a cylindrical shell with anisotropic conductivities.

Provided a new perspective for inverse design in wave systems.

Abstract

Illusion effects-where one object appears as another-arise from the non-uniqueness of physical systems, in which different material configurations yield identical external responses. Conventional approaches, such as coordinate transformation, map equivalent configurations but provide only specific solutions, while analytical or numerical optimization methods extend these designs by minimizing scattering yet remain constrained by model assumptions and computational cost. Here, we exploit this non-uniqueness through a data-driven framework that uses a variational autoencoder to compress high-dimensional thermal-field data into a compact latent space capturing geometrical relations between configurations and observations. In this latent space, thermal illusion corresponds to finding configurations that minimize geometric distance to a target configuration, with thermal cloaking as a special case where the target is free space. Specifically, we demonstrate the concept in a cylindrical shell with anisotropic thermal conductivities enclosing a core of arbitrary conductivity, achieving robust thermal illusion and cloaking using only positive conductivities. Such a latent-space distance approach provides a refreshed perspective for achieving illusion and can be applied to inverse-design problems in other classical wave systems.