TY - GEN
T1 - Deep Conservation
T2 - 35th AAAI Conference on Artificial Intelligence, AAAI 2021
AU - Lee, Kookjin
AU - Carlberg, Kevin T.
N1 - Funding Information:
This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Publisher Copyright:
Copyright © 2021, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85115669493
T3 - 35th AAAI Conference on Artificial Intelligence, AAAI 2021
SP - 277
EP - 285
BT - 35th AAAI Conference on Artificial Intelligence, AAAI 2021
PB - Association for the Advancement of Artificial Intelligence
Y2 - 2 February 2021 through 9 February 2021
ER -