Related papers: Stochastic Processes Under Linear Differential Con…

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…

Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace…

A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a…

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…

We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure…

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger…

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…