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.

翻译：数字孪生需要能够准确描述物理资产复杂动态且计算高效的低阶模型。然而，从含噪声的高维数据构建低阶模型具有挑战性。在这项工作中，我们提出一种数据驱动的非侵入式方法，该方法利用随机变分深度核学习从数据中发现低维潜在空间，并采用SVDKL的循环版本来表示和预测潜在动态的演化。所提出的方法通过两个具有挑战性的示例——双摆系统和反应-扩散系统——进行了验证。结果表明，我们的框架能够：（i）对测量值进行去噪和重建，（ii）学习系统状态的紧凑表示，（iii）在低维潜在空间中预测系统演化，以及（iv）量化建模不确定性。