Empirical Loss Weight Optimization for PINNModeling Laser Bio-effects on Human Skin for the 1D Heat Equation

J. Farmer, C. Oian, B. Bowman, & T. Khan

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.

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