Simulation and parameter optimization of the temperature field in mild moxibustion using physics-informed neural networks.

Accurate prediction of transient tissue temperature fields is important for understanding the thermal response of mild moxibustion and supporting treatment-parameter screening. In this study, a two-dimensional axisymmetric physics-informed neural network (PINN) model was developed to simulate bioheat transfer during mild moxibustion. The Pennes bioheat equation, layered tissue properties, and coupled radiation-convection boundary conditions at the skin surface were embedded into the loss function. Nine L9 (34) orthogonal cases were designed to evaluate the effects of moxa-burning temperature, moxa-stick diameter, moxibustion distance, and ambient temperature on the temperature response at a depth of 5 mm. The training processes showed stable convergence, and the average training time for a single parameter case was approximately 10 min. An additional confirmation case was compared with an independent COMSOL finite-element numerical benchmark at t = 1200 s. The mean absolute error, root-mean-square error, and maximum absolute error between the PINN and COMSOL temperature fields were 0.159, 0.299, and 2.723 °C, respectively. Range analysis showed that the influence of the four parameters followed the order of moxa-stick diameter > moxibustion distance > ambient temperature > moxa-burning temperature. The candidate parameter combination obtained under the present model conditions was 18 mm moxa-stick diameter, 25 mm moxibustion distance, 32 °C ambient temperature, and 650 °C moxa-burning temperature. These results suggest that the proposed PINN framework can provide a physics-constrained computational tool for temperature-field reconstruction and preliminary parameter screening in mild moxibustion, while further experimental and clinical validation remains necessary.