相关论文: Orbit Uncertainty Propagation and Sensitivity Anal…

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy…

The prohibitive cost of performing Uncertainty Quantification (UQ) tasks with a very large number of input parameters can be addressed, if the response exhibits some special structure that can be discovered and exploited. Several physical…

Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by…

A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…

This paper introduces a novel approach to uncertainty quantification for radiance fields by leveraging higher-order moments of the rendering equation. Uncertainty quantification is crucial for downstream tasks including view planning and…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However,…

We study stochastic dynamical systems in settings where only partial statistical information about the noise is available, e.g., in the form of a limited number of noise realizations. Such systems are particularly challenging to analyze and…

This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…

We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Linearly polarized emission is described, in general, in terms of the Stokes parameters $Q$ and $U$, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle…

Uncertainty in estimation of Drake Passage transport is analyzed in a Hessian-based uncertainty quantification (UQ) framework. The approach extends the adjoint-based ocean state estimation method to provide formal error bounds…

This thesis deals with the nonparametric estimation of density f of the regression error term E of the model Y=m(X)+E, assuming its independence with the covariate X. The difficulty linked to this study is the fact that the regression error…

We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…

This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…