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.

使用基于数据驱动的随机变分深度核学习以及递归版本，提出了一种构建 ROMs 的方法，能够对物理资产的复杂动态进行精确描述，并具备去噪、重建、学习紧凑表征系统状态、预测以及量化建模不确定性的能力。

动力系统的循环深度核学习

Recurrent Deep Kernel Learning of Dynamical Systems

Typically, voice conversion is regarded as an engineering problem with
limited training data. The reliance on massive amounts of data hinders the
practical applicability of deep learning approaches, which have been
extensively researched in recent years. On the other hand, statistical methods
are effective with limited data but have difficulties in modelling complex
mapping functions. This paper proposes a voice conversion method that works
with limited data and is based on stochastic variational deep kernel learning
(SVDKL). At the same time, SVDKL enables the use of deep neural networks'
expressive capability as well as the high flexibility of the Gaussian process
as a Bayesian and non-parametric method. When the conventional kernel is
combined with the deep neural network, it is possible to estimate non-smooth
and more complex functions. Furthermore, the model's sparse variational
Gaussian process solves the scalability problem and, unlike the exact Gaussian
process, allows for the learning of a global mapping function for the entire
acoustic space. One of the most important aspects of the proposed scheme is
that the model parameters are trained using marginal likelihood optimization,
which considers both data fitting and model complexity. Considering the
complexity of the model reduces the amount of training data by increasing the
resistance to overfitting. To evaluate the proposed scheme, we examined the
model's performance with approximately 80 seconds of training data. The results
indicated that our method obtained a higher mean opinion score, smaller
spectral distortion, and better preference tests than the compared methods.

基于随机变分深度核学习方法的有限数据语音转换模型在使用较少数据的情况下获得更高的平均意见得分、较小的频谱失真和更好的偏好测试结果。