  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.
