相关论文: Mesh refinement for uncertainty quantification thr…

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…

We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr…

Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases…

Many Multi-View-Stereo algorithms extract a 3D mesh model of a scene, after fusing depth maps into a volumetric representation of the space. Due to the limited scalability of such representations, the estimated model does not capture fine…

Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…

Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…

Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for…

The use of deep learning for medical imaging has seen tremendous growth in the research community. One reason for the slow uptake of these systems in the clinical setting is that they are complex, opaque and tend to fail silently. Outside…

Morden deep ensembles technique achieves strong uncertainty estimation performance by going through multiple forward passes with different models. This is at the price of a high storage space and a slow speed in the inference (test) time.…

We consider the problem of uncertainty quantification in change point regressions, where the signal can be piecewise polynomial of arbitrary but fixed degree. That is we seek disjoint intervals which, uniformly at a given confidence level,…

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using $k$-digits to the right from the decimal separator of a…

Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…

An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…

We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…