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

Authors

  • Kookjin Lee Sandia National Laboratories
  • Kevin T. Carlberg University of Washington

Keywords:

Natural Sciences

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.

Downloads

Published

2021-05-18

How to Cite

Lee, K., & Carlberg, K. T. (2021). Deep Conservation: A Latent-Dynamics Model for Exact Satisfaction of Physical Conservation Laws. Proceedings of the AAAI Conference on Artificial Intelligence, 35(1), 277-285. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/16102

Issue

Section

AAAI Technical Track on Application Domains