Effects of Training Data Source on PINN Modeling of Laser-Induced Heat Diffusion in Human Skin

Physics-informed neural networks (PINNs) have recently emerged as an effective surrogate to classical numerical methods for solving partial differential equations (PDEs) in a wide range of physical systems. When augmented with supervised data, PINN performance can depend strongly on the quality and characteristics of the training data; however, the influence of the numerical method used to generate that data remains largely unexplored. In this study, we investigate how training data generated by finite difference method (FDM) and finite element method (FEM) solvers affects PINN training and predictive accuracy, particularly in solving the one-dimensional heat equation under conditions relevant to laser–tissue interactions. A supervised data loss term is incorporated, and models trained on FDM- and FEM-generated temperature fields under identical physical conditions are compared to assess differences in convergence and accuracy. The results demonstrate that, under controlled one-dimensional diffusion settings, the numerical solver used for data generation produces a quantifiable, resolution-dependent effect on hybrid PINN performance: FDM-generated training data yields the lowest error across most tested resolutions, an advantage that narrows and becomes indistinguishable only at the finest resolution considered, providing practical guidance for selecting a data-generating solver in biological heat transfer applications.