Related papers: Modified noise kernels in Gaussian process modelli…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. Most approaches rely on iteratively denoising a Gaussian, a choice that may not…

This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…

The effective use of noisy intermediate-scale quantum devices requires error mitigation to improve the accuracy of sampled measurement distributions. The more accurately the effects of noise on these distributions can be modeled, the more…

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However,…

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress…

It has been observed that even a small amount of noise introduced into the dataset can significantly degrade the performance of KAN. In this brief note, we aim to quantitatively evaluate the performance when noise is added to the dataset.…

We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…

This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…

We consider identifiability of partially linear additive structural equation models with Gaussian noise (PLSEMs) and estimation of distributionally equivalent models to a given PLSEM. Thereby, we also include robustness results for errors…

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…

We consider the 1D Expected Improvement optimization based on Gaussian processes having spectral densities converging to zero faster than exponentially. We give examples of problems where the optimization trajectory is not dense in the…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…