Related papers: An Application of Gaussian Process Modeling for Hi…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
Many natural phenomena involve processes that happen simultaneously at different characteristic length- and timescales. Typically, the region where the process of interest happens is affected by fluctuations in its surroundings. Modeling…
Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…
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…
Graph condensation reduces the size of large graphs while preserving performance, addressing the scalability challenges of Graph Neural Networks caused by computational inefficiencies on large datasets. Existing methods often rely on…
Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
A significant advancement in nonlinear projection-based model order reduction (PMOR) is presented through a highly effective methodology. This methodology employs Gaussian process regression (GPR) and radial basis function (RBF)…
This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
3D reconstruction and simulation, although interrelated, have distinct objectives: reconstruction requires a flexible 3D representation that can adapt to diverse scenes, while simulation needs a structured representation to model motion…
In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory…
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a…
In this paper, we develop an adaptive Generalized Multiscale Discontinuous Galerkin Method (GMs-DGM) for a class of high-contrast flow problems, and derive a-priori and a-posteriori error estimates for the method. Based on the a-posteriori…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric…