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We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
This paper proposes a new 3D gas distribution mapping technique based on the local message passing of Gaussian belief propagation that is capable of resolving in real time, concentration estimates in 3D space whilst accounting for the…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
The recently proposed generalized epidemic modeling framework (GEMF) \cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…
We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…
We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is…
Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Numerical simulation of multi-phase fluid dynamics in porous media is critical for many energy and environmental applications in Earth's subsurface. Data-driven surrogate modeling provides computationally inexpensive alternatives to…
Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
Cooperative online scalar field mapping is an important task for multi-robot systems. Gaussian process regression is widely used to construct a map that represents spatial information with confidence intervals. However, it is difficult to…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
We present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding…
High-fidelity fracture mechanics simulations of multiple microcracks interaction via physics-based models quickly become computationally expensive as the number of microcracks increases. This work develops a Graph Neural Network (GNN) based…
Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance, especially for cell-edge users. In this work, we use stochastic geometry to analyze cooperation models where the positions of…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…