Multiscale Physics-Informed Neural Networks for the Inverse Design of Hyperuniform Optical Materials

TL;DR

This paper introduces multiscale physics-informed neural networks (MscalePINNs) for the inverse design of hyperuniform optical materials, enabling efficient retrieval of dielectric profiles and revealing transparency regions in finite-size photonic systems.

Contribution

The work extends high-frequency homogenization theory using MscalePINNs to design and analyze finite-size hyperuniform optical materials with isotropic responses.

Findings

MscalePINNs accurately capture complex field variations in hyperuniform structures.

Identification of a transparency region beyond long-wavelength approximation.

Effective isotropic homogenization achieved without disorder-averaging.

Abstract

In this article, we employ multiscale physics-informed neural networks (MscalePINNs) for the inverse design of finite-size photonic materials with stealthy hyperuniform (SHU) disordered geometries. Specifically, we show that MscalePINNs can capture the fast spatial variations of complex fields scattered by arrays of dielectric nanocylinders arranged according to isotropic SHU point patterns, thus enabling a systematic methodology to inversely retrieve their effective dielectric profiles. Our approach extends the recently developed high-frequency homogenization theory of hyperuniform media and retrieves more general permittivity profiles for applications-relevant finite-size SHU systems, unveiling unique features related to their isotropic nature. In particular, we numerically corroborate the existence of a transparency region beyond the long-wavelength approximation, enabling effective and isotropic homogenization even without disorder-averaging, in contrast to the case of uncorrelated Poisson random patterns. The flexible multiscale network approach introduced here enables the efficient inverse design of more general effective media and finite-size optical metamaterials with isotropic electromagnetic responses beyond the limitations of traditional homogenization theories.