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Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
The interpretation of seismic images faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Understanding uncertainties' role…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
Quality control (QC) of medical images is essential to ensure that downstream analyses such as segmentation can be performed successfully. Currently, QC is predominantly performed visually at significant time and operator cost. We aim to…
Removing geometrical details from a complex domain is a classical operation in computer aided design. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the…
Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To…
Recent advances in neural rendering have introduced numerous 3D scene representations. Although standard computer vision metrics evaluate the visual quality of generated images, they often overlook the fidelity of surface geometry. This…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…
Uncertainty in medical image segmentation is inherently non-uniform, with boundary regions exhibiting substantially higher ambiguity than interior areas. Conventional training treats all pixels equally, leading to unstable optimization…
Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
Provided a random realization of the cosmological model, observations of our cosmic neighborhood now allow us to build simulations of the latter down to the non-linear threshold. The resulting local Universe models are thus accurate up to a…
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
This paper presents a novel probabilistic voxel selection strategy for medical image registration in time-sensitive contexts, where the goal is aggressive voxel sampling (e.g. using less than 1% of the total number) while maintaining…
This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary…
We present Stochastic Gaussian Splatting (SGS): the first framework for uncertainty estimation using Gaussian Splatting (GS). GS recently advanced the novel-view synthesis field by achieving impressive reconstruction quality at a fraction…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…