Electromagnetic heating Processes (microwave and radio-frequency (RF) heating) are strongly nonlinear because of temperature-dependent dielectric characteristics and result in very non-uniform temperature distributions. The current literature mostly depends on the formulations of analytical studies or traditional numerical approaches that usually involve simplification of the assumptions or time-stepping schemes to address such nonlinear coupling. In this study, we develop a physics-informed deep learning framework to directly solve the fully coupled nonlinear electromagnetic–thermal system in a three-dimensional domain with temperature-dependent material properties. In contrast to the traditional method, the proposed approach does not require time discretization and offers a mesh-free solution by incorporating both the transient heat equation and the nonlinear electromagnetic power absorption term into the learning process. Three architectures, including standard physics-informed neural networks (PINN), gradient-enhanced PINN (gPINN) and extended PINN (XPINN) are designed and tested in the same physical conditions. The findings indicate that gPINN is more effective in sharpening thermal gradients and local non-uniformities whereas XPINN is more effective in converging and precision in the representation of multi-scale temperature fields. This work emphasizes how highly nonlinear coupled problems can be addressed with advanced physics-informed learning methods and offers a practical set of guidelines to choosing appropriate architectures in electromagnetic bio-thermal contexts.
Rizvi et al. (Sun,) studied this question.