Data Scoping: Effectively Learning the Evolution of Generic Transport PDEs

arXiv:2405.01319v1 Announce Type: new
Abstract: Transport phenomena (e.g., fluid flows) are governed by time-dependent partial differential equations (PDEs) describing mass, momentum, and energy conservation, and are ubiquitous in many engineering applications. However, deep learning architectures are fundamentally incompatible with the simulation of these PDEs. This paper clearly articulates and then solves this incompatibility. The local-dependency of generic transport PDEs implies that it only involves local information to predict the physical properties at a location in the next time step. However, …

abstract applications architectures arxiv conservation cs.ce cs.lg data deep learning differential energy engineering evolution however paper simulation the simulation transport type