Inverse Imaging and Illusion Control Assisted by Machine Learning

Abstract

Illusion refers to the effect of rendering an object indistinguishable from its background or another object to outside observers, thus concealing the original object. It enables devices like invisibility cloaks, with theoretical and experimental demonstrations through transformation approach and metamaterials. The opposite side of this effect is to recover the parameters of the original object from the observation data, a process termed inverse imaging. These two tasks, hiding and discovering, are generally considered opposing tasks and are thus addressed differently. In this thesis, we explore these two tasks under a unified topic from the perspective of the information contained in data. If the observation data capture sufficient information about a system, imaging is possible, while illusion can arise when the observations reveal no information about an object’s real configuration. It is therefore possible to tackle both sides via the same data-driven method.

Before diving into the unified data-driven method, we first employ the analytical method, transformation approach, to realize and better understand illusion effect. We achieve illusion effect on curved surfaces in systems governed by Helmholtz equation by building equivalence between the curvature and isotropic material indices via coordinate mapping. This is experimentally verified in flexural waves, where a curved plate behaves like a flat plate or another curved plate with distinct shape by prescribing thickness variations through our theory. This approach extends the merit of using isotropic material indices to achieve field transformation from two-dimensional flat surfaces to curved surfaces embedded in three-dimensional space, thus providing a feasible way to control physical fields on curved surfaces.

Then, we propose to use the artificial neural network-based unsupervised machine learning method, variational autoencoder, to tackle both imaging and illusion. The variational autoencoder features compressing the observation data into a highly compact and regular latent space. Such a latent space can be leveraged to evaluate whether the mapping from the observation data to the physical parameters is unique by finding the number of degrees of freedom in data. If the mapping is unique, we can achieve inverse imaging, as we demonstrate in the imaging problem with flexural waves to extract material and geometrical parameters by converting the latent variables into their independent representations through independent component analysis in a further step. If the mapping is not unique, illusion can occur, since producing the same observation through different physical configurations enables illusion phenomena. We exploit such non-uniqueness to design thermal illusion devices that disguise an object as the background or another object by establishing equivalence between different system configurations through measuring the geometrical distance in latent space. Furthermore, this method can be applied to discover physically meaningful quantities aligned with analytical understanding even from data with incomplete information. We demonstrate such a case in the discovery of effective permittivity and permeability in optical layered systems from the collected electric fields by cascading variational autoencoder and independent component analysis, which can bypass analytical derivations based on governing equations. This unified approach offers a versatile tool to evaluate information in observation data, and may find applications in data-driven discovery of physics by leveraging the extracted meaningful quantities, for example, to facilitate building physical models from complex data, with potential to bridge machine learning results and analytical understanding.

Date of Award	2025
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Jensen Tsan Hang LI (Supervisor) & Che Ting CHAN (Supervisor)