Empirical loss weight optimization for PINN modeling laser bio-effects on human skin for the 1D heat equation

Abstract

The application of deep neural networks towards solving problems in science and engineering has demonstrated encouraging results with the recent formulation of physics-informed neural networks (PINNs). Through the development of refined machine learning techniques, the high computational cost of obtaining numerical solutions for partial differential equations governing complicated physical systems can be mitigated. However, solutions are not guaranteed to be unique, and are subject to uncertainty caused by the choice of network model parameters. For critical systems with significant consequences for errors, assessing and quantifying this model uncertainty is essential. In this paper, an application of PINN for laser bio-effects with limited training data is provided for uncertainty quantification analysis. Additionally, an efficacy study is performed to investigate the impact of the relative weights of the loss components of the PINN and how the uncertainty in the predictions depends on these weights. Network ensembles are constructed to empirically investigate the diversity of solutions across an extensive sweep of hyper-parameters to determine the model that consistently reproduces a high-fidelity numerical simulation.

Keywords

• Uncertainty quantification
• PINN
• Loss weights
• Machine learning
• Heat diffusion equation