Recurrent Deep Kernel Learning of Dynamical Systems

TL;DR

A data-driven, non-intrusive method that utilizes stochastic variational deep kernel learning (SVDKL) to discover low-dimensional latent spaces from data and a recurrent version of SVDKL for representing and predicting the evolution of latent dynamics.

Abstract

Digital twins require computationally-efficient reduced-order models (ROMs) that can accurately describe complex dynamics of physical assets. However, constructing ROMs from noisy high-dimensional data is challenging. In this work, we propose a data-driven, non-intrusive method that utilizes stochastic variational deep kernel learning (SVDKL) to discover low-dimensional latent spaces from data and a recurrent version of SVDKL for representing and predicting the evolution of latent dynamics. The proposed method is demonstrated with two challenging examples -- a double pendulum and a reaction-diffusion system. Results show that our framework is capable of (i) denoising and reconstructing measurements, (ii) learning compact representations of system states, (iii) predicting system evolution in low-dimensional latent spaces, and (iv) quantifying modeling uncertainties.

Figures (13)

• Figure 1: Proposed framework for reduced-order modeling of dynamical systems. We encode the measurements $\mathbf{x}_t$ at different time instances into the latent variables $\mathbf{z}_t$ by means of a deep kernel learning encoder. Then, we feed a sequence of length $H$ of consecutive latent variables $\mathbf{z}_{t-H:t}$, actions $\mathbf{u}_{t-H:t}$, and parameters $\mathbf{p}$ to a recurrent deep kernel learning to predict the next latent variable $\mathbf{z}_{t+1}$. The measurements are then reconstructed $\hat{\mathbf{x}}$ by means of a decoder from the latent variables.
• Figure 2: Architecture of the SVDKL encoder.
• Figure 3: Architecture of the decoder.
• Figure 4: Architecture of the forward dynamical model.
• Figure 5: Double pendulum and reaction-diffusion systems.