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

Abstract

In this study, multiscale physics-informed neural networks (MscalePINNs) are employed for the inverse design of finite-size photonic materials with stealthy hyperuniform (SHU) disordered geometries. Specifically, MscalePINNs are shown to 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. This approach extends the recently developed high-frequency homogenization theory of hyperuniform media and retrieves more general permittivity profiles for applications-relevant finite-size SHU and optical systems, unveiling unique features related to their isotropic nature. In particular, the existence of a transparency region beyond the long-wavelength approximation is numerically corroborated, enabling the retrieval of effective and isotropic locally homogeneous media 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.