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Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is…
The Multi-Output Gaussian Process is is a popular tool for modelling data from multiple sources. A typical choice to build a covariance function for a MOGP is the Linear Model of Coregionalization (LMC) which parametrically models the…
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
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…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…
Pareto Front (PF) modeling is essential in decision making problems across all domains such as economics, medicine or engineering. In Operation Research literature, this task has been addressed based on multi-objective optimization…
Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
Wireless power transfer (WPT) with coupled resonators offers a promising solution for the seamless powering of electronic devices. Interactive design approaches that visualize the magnetic field and power transfer efficiency based on system…
Despite the increased computational resources, the simulation-based design optimization (SBDO) procedure can be very expensive from a computational viewpoint, especially if high-fidelity solvers are required. Multi-fidelity metamodels have…
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…