Physics-informed neural networks for inverse problems in nano-optics and metamaterials

Abstract

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nanooptics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the Finite Element Method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories. *

Deep Learning the Electromagnetic Properties of Metamaterials—A Comprehensive Review

“…[ 150 ] These specialized models, including the recently introduced physics‐informed neural networks (PINNs), [ 163 ] are an exciting and emerging area of research within DL (see Section 6), but are still relatively early in development with few applications to problems in electromagnetism and AEM systems. [ 164,165 ]…”

“…The authors in refs. [164,165] applied a newly‐developed framework termed physics‐informed neural networks (PINNs) [ 163 ] to solve challenging problems involving the inference of the permittivity or permeability parameters of a metamaterial that give rise to a particular set of field measurements. This is a challenging problem that is difficult to solve using other approaches, including conventional DNNs.…”

Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations

“…These networks are referred to as physics-informed neural networks (PINNs). Such networks have found application throughout science and engineering, including fluid dynamics [24] , [23] , [25] , material electromagnetic property discovery [8] , acoustic waves [31] , nonlinear diffusivity [11] , material fatigue [32] , and dynamical systems [21] . Very recently, initial investigations have been made into encoding solutions parametrically as , for θ some set of solution variables [28] ; θ may include domain shape, physical properties, or boundary condition parameters.…”

A physics-informed neural network for sound propagation in the atmospheric boundary layer

“…The closest PINN application the authors found was in the inference of optical impedance in a metamaterial based on scattering predictions from a high-fidelity finite element model. 9 It should be noted that the PINN model was not used to predict scattered optical field; rather, the Helmholtz equation served as the physics-informed loss function, and the optical impedance of the meta-material was a training parameter that the optimizer was free to adjust as the loss function was reduced to better satisfy the Helmholtz equation.…”