Related papers: Gaussian Process Regression for Uncertainty Quanti…

Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce…

Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they…

This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple examples, which are understandable to undergraduates, to…

With the advancement of GPS, remote sensing, and computational simulations, large amounts of geospatial and spatiotemporal data are being collected at an increasing speed. Such emerging spatiotemporal big data assets, together with the…

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate expensive electronic structure calculations. The key idea is to…

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…

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…

In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes…

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

This paper presents a probabilistic surrogate model for the accelerated design of electric vehicle battery enclosures with a focus on crash performance. The study integrates high-throughput finite element simulations and Gaussian Process…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs)…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…

If Uncertainty Quantification (UQ) is crucial to achieve trustworthy Machine Learning (ML), most UQ methods suffer from disparate and inconsistent evaluation protocols. We claim this inconsistency results from the unclear requirements the…