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Recently, 3D Gaussian Splatting (3DGS) has emerged as an efficient approach for accurately representing scenes. However, despite its superior novel view synthesis capabilities, extracting the geometry of the scene directly from the Gaussian…
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
Numerical simulation of complex optical structures enables their optimization with respect to specific objectives. Often, optimization is done by multiple successive parameter scans, which are time consuming and computationally expensive.…
The equilibrium free energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is…
We describe a procedure for constructing a model of a smooth data spectrum using Gaussian processes rather than the historical parametric description. This approach considers a fuller space of possible functions, is robust at increasing…
The free energetics of water density fluctuations near a surface, and the rare low-density fluctuations in particular, serve as reliable indicators of surface hydrophobicity; the easier it is to displace the interfacial waters, the more…
Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, as well as quantum tunneling phenomena. The most common theoretical…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Branches swaying in the breeze, flags rippling in the wind, and boats rocking on the water all show how aerodynamics shape natural motion -- an effect crucial for realism in vision and graphics. In this paper, we present Gaussian Swaying, a…
While Gaussian Splatting (GS) demonstrates efficient and high-quality scene rendering and small area surface extraction ability, it falls short in handling large-scale aerial image surface extraction tasks. To overcome this, we present…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
We present a framework that enables fast reconstruction and real-time rendering of urban-scale scenes while maintaining robustness against appearance variations across multi-view captures. Our approach begins with scene partitioning for…