相关论文: Uncertainty Quantification of Darcy Flow through P…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface…

We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are…

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…

Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…

Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent…

Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…

In this work, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on the Gaussian Process (GP) learning to understand the power system behavior under uncertainty for better operational decisions. The technique can…

Obtaining accurate water level predictions are essential for water resource management and implementing flood mitigation strategies. Several data-driven models can be found in the literature. However, there has been limited research with…

Gaussian processes (GPs) are widely used as surrogate models for emulating computer code, which simulate complex physical phenomena. In many problems, additional boundary information (i.e., the behavior of the phenomena along input…

The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…

The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To…

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

We present Flow-Induced Diagonal Gaussian Processes (FiD-GP), a compression framework that incorporates a compact inducing weight matrix to project a neural network's weight uncertainty into a lower-dimensional subspace. Critically, FiD-GP…