Physics-Constrained Deep Autoencoded Kalman Filters for Estimating Vapor Compression System States

Physics-based computational models of vapor compression systems (VCSs) enable high-fidelity simulations but require high-dimensional state representations. The underlying VCS dynamics are stiff, constrained by conservation laws, and only a small fraction of states can be measured. While recent advances on constrained extended Kalman filtering (EKF) have provided a systematic framework for estimating VCS states via simulation models, two major bottlenecks to efficient implementation include: (i) expensive forward predictions requiring customized stiff solvers; and, (ii) frequent and computationally expensive linearization operations on high-dimensional nonlinear models. In this letter, we circumvent these bottlenecks by constructing deep autoencoder (AE)-based state-space models (SSMs) from simulation data for which both forward predictions and linearization operations via automatic differentiation can be performed efficiently. In addition, we incorporate physical constraints based on pressure gradients explicitly into the autoencoder, and demonstrate, on a Julia-based high-fidelity simulator, that the physics-constrained model improves the estimation performance compared to a AE-based SSM that does not enforce physics.