One-Dimensional Radiative Transfer Equation Solution by Physics-Informed Neural Networks: Performance Analysis

Physics-Informed Neural Networks (PINNs) provide a powerful framework for solving partial differential equations (PDEs) across various scientific and engineering disciplines. Unlike traditional numerical methods, PINNs do not require extensive expertise in the underlying numerical techniques of the target domain, making them accessible for a broader range of users. While PINNs have shown promise for solving forward and inverse problems, their performance relative to classical methods remains a topic of active investigation, particularly in radiative transfer applications. In this study, we assess the application of PINNs to a one-dimensional radiative transfer equation. Through simple test cases, we evaluate their strengths and limitations compared to the discrete ordinate method. Our findings indicate that PINNs can achieve an error as low as 0.3 % within several minutes of computation, whereas traditional solvers are significantly faster. However, the ease of implementation and the ability of PINNs to address inverse and high-dimensional problems highlight their potential as a complementary approach, particularly for complex scenarios.