A physics-informed neural network (PINN) is developed to estimate the spatially varying parameters of the time-dependent heat equation in one dimension. The proposed model incorporates both the forward and inverse problems to estimate the temperature and thermal properties of a laser-induced interaction with biological tissue. The network can detect the presence and location of a second layer of tissue, if it exists, and estimate the thermal coefficients of each substance. This ability to model nonhomogeneous properties in tissue subjected to laser irradiation has many important applications in medical procedures. An ensemble method is used to quantify the epistemic uncertainty of all estimates to identify weaknesses in the model. Aleotoric uncertainty is simulated through noise perturbations, demonstrating robust estimates in the presence of measurement error. The uncertainty associated with parameter estimation provides insight into the ill-posedness of the inverse problem.
Farmer et al. (2026) studied this question.