Related papers: A New Class of High-Order Methods for Fluid Dynami…

This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…

Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of…

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

Quadrature-based moment-closure methods are a class of approximations that replace high-dimensional kinetic descriptions with lower-dimensional fluid models. In this work we investigate some of the properties of a sub-class of these methods…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…

Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are…

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…

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows. The finite volume method (FVM) is an important one. In FVM, space is discretized to many grid cells. When the number of grid…

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with the stiff Poisson equations. In this article we use CGP for the first…

We address the task of simultaneous feature fusion and modeling of discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GP encoders to project multiple observed…

Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original…

Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost…

In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…

Traditional explicit 3D representations, such as point clouds and meshes, demand significant storage to capture fine geometric details and require complex indexing systems for surface lookups, making functional representations an efficient,…