Auxiliary Physics-Informed Neural Networks for Forward, Inverse, and Coupled Radiative Transfer Problems

TL;DR

This paper introduces auxiliary physics-informed neural networks (APINNs) to efficiently solve forward, inverse, and coupled radiative transfer problems involving complex scattering media, with applications in thermal transport and biomedical imaging.

Contribution

The paper presents a novel APINN framework that handles integro-differential radiative transfer equations with multiple auxiliary variables, expanding the capabilities of physics-informed neural networks.

Findings

Successfully solves Boltzmann-type transport equations with multi-output neural networks.

Demonstrates application to coupled radiation-conduction problems with non-Fourier temperature profiles.

Retrieves single scattering albedo from boundary data in inverse problems.

Abstract

In this paper, we develop and employ auxiliary physics-informed neural networks (APINNs) to solve forward, inverse, and coupled integro-differential problems of radiative transfer theory (RTE). Specifically, by focusing on the relevant slab geometry and scattering media described by different types of phase functions, we show how the proposed APINN framework enables the efficient solution of Boltzmann-type transport equations through multi-output neural networks with multiple auxiliary variables associated to the Legendre expansion terms of the considered phase functions. Furthermore, we demonstrate the successful application of APINN to the coupled radiation-conduction problem of a participating medium and find distinctive temperature profiles beyond the Fourier thermal conduction limit. Finally, we solve the inverse problem for the Schwarzschild-Milne integral equation and retrieve the single scattering albedo based solely on the knowledge of boundary data, similar to what is often available in experimental settings. The present work significantly expands the current capabilities of physics-informed neural networks for radiative transfer problems that are relevant to the design and understanding of complex scattering media and photonic structures with applications to metamaterials, biomedical imaging, thermal transport, and semiconductor device modeling.