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

No. 1: AAAI-21 Technical Tracks 1

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 35

AAAI Technical Track on Application Domains

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.

10.1609/aaai.v35i1.16102