Numerical Solution and Uncertainty Quantification of Bioheat Transfer Equation Using Neural Network Approach

The paper deals with a novel approach to carry out uncertainty quantification in modeling of bioheat transfer equation using neural networks and deep learning. The output uncertainty is achieved via Monte Carlo (MC) dropout procedure using Bayesian inference, while the input uncertainty propagation is achieved using MC simulation of the ensemble of physics-informed neural networks (PINNs). The proposed approach uses a neural network with integrated physical knowledge without need of any prior assumptions and mesh generation, respectively. Deterministic modeling is related to both analytical and numerical (finite element method) solution of bioheat transfer equation. The computational example considered in this work pertains to the solution of rather simple one-dimensional problem of bioheat transfer, as a kind of opener to the subject.