相关论文: Pressure reconstruction from error-embedded gradie…

This paper presents a real-time capable algorithm for the learning of Gaussian Processes (GP) for submodels. It extends an existing recursive Gaussian Process (RGP) algorithm which requires a measurable output. In many applications,…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…

In this paper, we propose \texttt{FGPR}: a Federated Gaussian process ($\mathcal{GP}$) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local client computations. Notably, the…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…

We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a…

This manuscript addresses the challenge of designing functionally graded materials (FGMs) for arbitrary-shaped domains. Towards this goal, the present work proposes a generic volume fraction profile generation algorithm based on Gaussian…

We develop a novel framework to accelerate Gaussian process regression (GPR). In particular, we consider localization kernels at each data point to down-weigh the contributions from other data points that are far away, and we derive the GPR…

Accurate channel estimation with low pilot overhead and computational complexity is key to efficiently utilizing multi-antenna wireless systems. Motivated by the evolution from purely statistical descriptions toward physics- and…

Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…

The increase of discrepancy in the standard procedure to choose the arbitrary functional form of the Lagrangian $f(Q)$ motivates us to solve this issue in modified theories of gravity. In this regard, we investigate the Gaussian process…

Accurately representing the sound field with the high spatial resolution is critical for immersive and interactive sound field reproduction technology. To minimize experimental effort, data-driven methods have been proposed to estimate…

In this paper, we treat the problem of evaluating the asymptotic error in a numerical integration scheme as one with inherent uncertainty. Adding to the growing field of probabilistic numerics, we show that Gaussian process regression (GPR)…

The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization…

We use a Gaussian Process Regression (GPR) strategy that was recently developed [3,16,17] to analyze different types of curves that are commonly encountered in parametric eigenvalue problems. We employ an offline-online decomposition…

Gaussian splatting has gained attention for its efficient representation and rendering of 3D scenes using continuous Gaussian primitives. However, it struggles with sparse-view inputs due to limited geometric and photometric information,…

Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…

Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are…

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…