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Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Task learning in neural networks typically requires finding a globally optimal minimizer to a loss function objective. Conventional designs of swarm based optimization methods apply a fixed update rule, with possibly an adaptive step-size…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
We propose to recover spectral details from RGB images of known spectral quantization by modeling natural spectra under Gaussian Processes and combining them with the RGB images. Our technique exploits Process Kernels to model the relative…
Reconstructing high-fidelity underwater scenes remains a challenging task due to light absorption, scattering, and limited visibility inherent in aquatic environments. This paper presents an enhanced Gaussian Splatting-based framework that…
In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty…
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.…
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…
A new simulated tempering method, which is referred to as simulated tempering umbrella sampling, for calculating the free energy of chemical reactions is proposed. First principles molecular dynamics simulations with this simulated…
The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data…
While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…
3D Gaussian Splatting (3DGS) has demonstrated impressive performance in scene reconstruction. However, most existing GS-based surface reconstruction methods focus on 3D objects or limited scenes. Directly applying these methods to…
Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage…