TENG: Time-Evolving Natural Gradient for Solving PDEs with Deep Neural Net

arXiv:2404.10771v1 Announce Type: new
Abstract: Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the $\textit{Time-Evolving Natural Gradient (TENG)}$, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimization to obtain high accuracy in neural-network-based PDE solutions. Our comprehensive development includes algorithms like TENG-Euler …

abstract accuracy arxiv challenges complexities cs.lg differential engineering gradient modeling natural networks neural net neural networks paper physics.comp-ph science shift systems type value