Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks

arXiv:2105.00862v2 Announce Type: replace
Abstract: Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that PINNs are difficult to train and often require a careful tuning of loss weights when data and physics loss functions are combined by scalarization of a multi-objective (MO) problem. In this paper, we aim to understand how parameters of the physical system, such …

abstract advance arxiv cs.lg data deep learning differential front networks neural networks pareto physics physics-informed replace train type