Deep Conservation: A Latent-Dynamics Model for Exact Satisfaction of Physical Conservation Laws

Kookjin Lee, Kevin T. Carlberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system state using deep convolutional autoencoders. This defines a low-dimensional nonlinear manifold on which the state is subsequently enforced to evolve. Second, the method defines a latent-dynamics model that associates with the solution to a constrained optimization problem. Here, the objective function is defined as the sum of squares of conservation-law violations over control volumes within a finite-volume discretization of the problem; nonlinear equality constraints explicitly enforce conservation over prescribed subdomains of the problem. Under modest conditions, the resulting dynamics model guarantees that the time-evolution of the latent state exactly satisfies conservation laws over the prescribed subdomains.

Original languageEnglish (US)
Title of host publication35th AAAI Conference on Artificial Intelligence, AAAI 2021
PublisherAssociation for the Advancement of Artificial Intelligence
Pages277-285
Number of pages9
ISBN (Electronic)9781713835974
StatePublished - 2021
Externally publishedYes
Event35th AAAI Conference on Artificial Intelligence, AAAI 2021 - Virtual, Online
Duration: Feb 2 2021Feb 9 2021

Publication series

Name35th AAAI Conference on Artificial Intelligence, AAAI 2021
Volume1

Conference

Conference35th AAAI Conference on Artificial Intelligence, AAAI 2021
CityVirtual, Online
Period2/2/212/9/21

ASJC Scopus subject areas

  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'Deep Conservation: A Latent-Dynamics Model for Exact Satisfaction of Physical Conservation Laws'. Together they form a unique fingerprint.

Cite this