Related papers: Gaussian Processes for Inferring Parton Distributi…

Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…

Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…

A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the…

This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

Gaussian process regression (GPR) is a useful technique to predict composition--property relationships in glasses as the method inherently provides the standard deviation of the predictions. However, the technique remains restricted to…

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD…

We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing…

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first…

We apply the Lagrange Multiplier method to study the uncertainties of physical predictions due to the uncertainties of parton distribution functions (PDFs), using the cross section for W production at a hadron collider as an archetypal…

Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…

We propose an analysis method for the leading-twist operator product expansion based lattice QCD determinations of the valence parton distribution function (PDF). In the first step, we determine the confidence-intervals of the leading-twist…

Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…

We present a detailed study of the helicity-dependent and helicity-independent collinear parton distribution functions (PDFs) of the nucleon, using the quasi-PDF approach. The lattice QCD computation is performed employing twisted mass…

We review recent progress towards a determination of a set of polarized parton distributions from a global set of deep-inelastic scattering data based on the NNPDF methodology, in analogy with the unpolarized case. This method is designed…

Generalized parton distributions (GPDs) are key quantities for the description of a hadron's three-dimensional structure. They are the current focus of all areas of hadronic physics -- phenomenological, experimental, and theoretical,…