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Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Predicting the forced vibration response of nonlinear mechanical systems with friction is critical for engineering applications. Accurately determining the backbone curve of resonance peaks is pivotal for the design of friction devices.…

We introduce MGP-VAE (Multi-disentangled-features Gaussian Processes Variational AutoEncoder), a variational autoencoder which uses Gaussian processes (GP) to model the latent space for the unsupervised learning of disentangled…

The functional ANOVA expansion of a multivariate mapping plays a fundamental role in statistics. The expansion is unique once a unique distribution is assigned to the covariates. Recent investigations in the environmental and climate…

The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours…

Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…

Electroencephalogram (EEG)-based emotion recognition holds significant value in affective computing and brain-computer interfaces. However, in practical applications, EEG recordings are susceptible to the effects of various physiological…

We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric…

Global Sensitivity Analysis (GSA) is the study of the influence of any given inputs on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of…

This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…

Gaussian process (GP) is arguably one of the most widely used machine learning algorithms in practice. One of its prominent applications is Bayesian optimization (BO). Although the vanilla GP itself is already a powerful tool for BO, it is…

Functional data describe a wide range of processes, such as growth curves and spectral absorption. In this study, we analyze air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions…

To reduce computational overhead while maintaining model performance, model pruning techniques have been proposed. Among these, structured pruning, which removes entire convolutional channels or layers, significantly enhances computational…

This paper proposes a component-based dual decomposition of the nonconvex AC optimal power flow (OPF) problem, where the modified dual function is solved in a distributed fashion. The main contribution of this work is that is demonstrates…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

The rise of electron microscopy has expanded our ability to acquire nanometer and atomically resolved images of complex materials. The resulting vast datasets are typically analyzed by human operators, an intrinsically challenging process…

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…

The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…