Related papers: Random boundaries: quantifying segmentation uncert…

Deep learning motivated by convolutional neural networks has been highly successful in a range of medical imaging problems like image classification, image segmentation, image synthesis etc. However for validation and interpretability, not…

This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

The production of thematic maps depicting land cover is one of the most common applications of remote sensing. To this end, several semantic segmentation approaches, based on deep learning, have been proposed in the literature, but land…

A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…

Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to…

This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…

Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…

Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…

Equipping predicted segmentation with calibrated uncertainty is essential for safety-critical applications. In this work, we focus on capturing the data-inherent uncertainty (aka aleatoric uncertainty) in segmentation, typically when…

In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to…

Graph Neural Networks (GNNs) can predict the performance of an industrial design quickly and accurately and be used to optimize its shape effectively. However, to fully explore the shape space, one must often consider shapes deviating…

We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to…