Physics-Informed Neural Networks for Radiative Transfer and Boltzmann Transport Problems of Optoelectronic Device Modeling

There is a growing interest in developing deep learning (DL) and artificial intelligence (AI) algorithms for electromagnetic wave engineering and materials design. Rapidly emerging approaches include training artificial neural networks (ANNs) to solve inverse problems and parameter estimation in complex photonic environments. Although successfully demonstrated at solving several inverse design problems, traditional DL methods are essentially data-driven techniques requiring time-consuming training steps that use massive datasets. Moreover, in order to improve on purely data-driven methods, it is important to constrain and regularize them by leveraging the underlying physics of the investigated problems. Here we discuss our advances in building a robust framework for the design of photonic materials and devices based on auxiliary physics-informed neural networks (APINNs) for the accurate solution of complex forward and inverse problems in electromagnetic scattering and radiative transfer theory. In particular, we introduce and discuss APINNs architectures for the inverse solution of high-dimensional integro-differential Boltzmann-type transport problems of relevance to optoelectronic devices and optical materials design and we demonstrate efficient parameter estimation in coupled conductive-radiative systems with applications to heat transfer in semiconductor devices. Specifically, we employ APINNs to solve the phonon Boltzmann transport equation (BTE) for AlGaN alloys in different geometries. Our work shows that APINNs possess the flexibility, accuracy, and noise robustness required to become a powerful design approach for inverse scattering and the non-local thermal modeling of optoelectronic devices beyond the Fourier thermal transport limit. The presented work expands upon the current capabilities and range of applications of physics-informed neural networks and paves the way to the study of complex transport problems and light-matter interactions in strongly scattering media with applications to nanophotonics, biomedical imaging, and semiconductor device modeling.