Deep adaptive sampling for surrogate modeling without labeled data

arXiv:2402.11283v1 Announce Type: cross
Abstract: Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a promising direction due to its potential to handle high dimensionality, which requires minimizing a loss over a training set of random samples. However, the random samples introduce statistical errors, which may become the dominant errors for the approximation of low-regularity and high-dimensional problems. In …

abstract arxiv construct contrast cs.na data deep learning differential differential equation dimensionality equation loss math.na modeling numerical parametric physics physics-informed practical sampling significance stat.ml systems type