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Physics informed neural networks to solve radiative transfer equation in absorbing-scattering media

par Biswal, Pratibha ;Avdijaj, Jetnis ;Parente, Alessandro ;Coussement, Axel
Référence Journal of quantitative spectroscopy & radiative transfer, 344, 109509
Publication Publié, 2025-10-01

Article révisé par les pairs

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Résumé :

Physics-informed neural networks have emerged as powerful tools for addressing complex forward and inverse problems governed by partial differential equations (PDEs). By embedding PDEs into the neural network's loss function through automatic differentiation, PINN enables efficient evaluation at scattered spatio-temporal residual points. In this study, PINN methods are applied to solve integro-differential equations in the form of radiative transfer equations (RTE), focusing on radiation in gaseous scattering media typical of high-temperature furnace environments. The scattering phase function is expanded using Legendre polynomials, and the Gauss–Legendre quadrature method is employed to accurately compute the integral terms. Both ADAM and L-BFGS optimization techniques are used. Sobol sampling is utilized for efficient residual point selection. Additionally, radiation heat balance on furnace walls is incorporated to ensure physical accuracy in 2D models. Five case studies are explored, covering scenarios of non-absorbing, absorbing, non-scattering, and scattering media to investigate the behavior of radiation transfer under varying conditions. The effects of absorption and scattering coefficients on radiation heat flux are thoroughly analyzed, and results are compared to previous models. The findings from this study provide valuable insights and practical guidelines for solving RTE in similar high-temperature applications.