Zero Coordinate Shift: Whetted Automatic Differentiation for Physics-informed Operator Learning

arXiv:2311.00860v3 Announce Type: replace
Abstract: Automatic differentiation (AD) is a critical step in physics-informed machine learning, required for computing the high-order derivatives of network output w.r.t. coordinates of collocation points. In this paper, we present a novel and lightweight algorithm to conduct AD for physics-informed operator learning, which we call the trick of Zero Coordinate Shift (ZCS). Instead of making all sampled coordinates as leaf variables, ZCS introduces only one scalar-valued leaf variable for each spatial or temporal dimension, simplifying …

abstract algorithm arxiv call computing cs.ai cs.lg cs.na derivatives differentiation machine machine learning math.na network novel paper physics physics.comp-ph physics-informed shift type