Recurrent Deep Kernel Learning of Dynamical Systems

TL;DR

This paper introduces a novel deep kernel learning approach for dynamical systems that efficiently models complex, noisy data, enabling accurate predictions and uncertainty quantification in reduced-order models.

Contribution

It presents a non-intrusive, data-driven recurrent deep kernel learning method for discovering low-dimensional latent spaces and predicting system dynamics.

Findings

Effective denoising and reconstruction of measurements

Learning compact low-dimensional representations

Accurate prediction of system evolution and uncertainty quantification

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.