Physics-Informed Neural Networks for the Photon Linear Boltzmann Transport Equation: A Feasibility Study for Medical Physics

Ayoub El Abbassi¹*, Mustapha Krim¹, Youssef Bouzekraoui¹, Abdessamad Didi¹

¹ Laboratory of Health Sciences and Technologies (LSTS), Higher Institute of Health Sciences (ISSS), Hassan First

University of Settat, Settat, Morocco.

*Corresponding author: Ayoub El Abbassi; E-mail: ayoub.elabbassi.phys@gmail.com

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Abstract

Accurate radiation transport modeling is critical for precise dose calculation in medical physics. While the Linear Boltzmann Transport Equation (LBTE) provides the foundational framework for particle transport, its high-dimensional integro-differential structure imposes severe computational and memory difficulties, motivating the investigation of alternative solution strategies. In this work, we systematically evaluate Physics-Informed Neural Networks (PINNs) as mesh-free solvers for stationary photon transport, specifically to assess their ability to approximate the photon fluence (LBTE solution) as a fundamental intermediate quantity for dose calculation. Rather than relying on a single generic architecture, we introduced targeted physics-informed strategies to address localized angular sources, sharp material interfaces, multigroup energy coupling, and the computational burden of three-dimensional angular integration. Benchmarked against the OpenSN transport code and reference solutions from the literature, the results demonstrate that PINNs can accurately reproduce a broad range of deterministic photon-transport solutions when the formulation is adapted to the underlying transport structure. These findings establish a proof of concept for PINN-based photon transport in medical physics and provide a methodological foundation for their further development toward generalizable transport solutions and, ultimately, dose-calculation frameworks.

Keywords: Medical Physics; Physics-Informed Neural Networks; Boltzmann Transport Equation; Photon Transport; Radiotherapy; OpenSN; Multigroup Optimization; Fourier Features.

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