Related papers: Physics-constrained Gaussian Processes for Predict…

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…

In the preceding paper [T. Fabcic et al., preprint] "restricted Gaussian wave packets" were introduced for the regularized Coulomb problem in the four-dimensional Kustaanheimo-Stiefel coordinates, and their exact time propagation was…

Calibrating for direction-dependent ionospheric distortions in visibility data is one of the main technical challenges that must be overcome to advance low-frequency radio astronomy. In this paper, we propose a novel probabilistic,…

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Quantum molecular dynamic simulations have been employed to study the equation of state (EOS) of fluid helium under shock compressions. The principal Hugoniot is determined from EOS, where corrections from atomic ionization are added onto…

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…

Recent research has proven neural networks to be a powerful tool for performing hyperspectral imaging (HSI) target identification. However, many deep learning frameworks deliver a single material class prediction and operate on a per-pixel…

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…

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…

Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…

We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use available $H(z)$ observations from (i) cosmic chronometers data (CC); (ii) Supernova Type Ia (SN) data from the…

This paper outlines an approach towards improved rigour in tokamak turbulence transport model validation within integrated modelling. Gaussian process regression (GPR) techniques were applied for profile fitting during the preparation of…

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies…