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In order to predict future performance of subsurface fluid reservoirs under possible operating scenarios, a dynamic, porous-medium flow simulation model must be tuned to include representative properties of the reservoir. Estimating…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

Spatially-indexed multivariate data appear frequently in geostatistics and related fields including oceanography and environmental science. To take full advantage of this data structure, cross-covariance functions are constructed to…

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…

We propose an approach to use the state covariance of linear systems to track time-varying covariance matrices of non-stationary time series. Following concepts from Riemmanian geometry, we investigate three types of covariance paths…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…

During the Gaussian Splatting optimization process, the scene's geometry can gradually deteriorate if its structure is not deliberately preserved, especially in non-textured regions such as walls, ceilings, and furniture surfaces. This…

We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…

In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…

Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…