  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.
