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Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often…

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to…

In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for…

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…

Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more and more groups attempting to understand the uncertainties on their calculations. However, recent studies have shown that…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…

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…

In this paper, we present an uncertainty-aware INVASE to quantify predictive confidence of healthcare problem. By introducing learnable Gaussian distributions, we lever-age their variances to measure the degree of uncertainty. Based on the…

To model and quantify the variability in plasticity and failure of additively manufactured metals due to imperfections in their microstructure, we have developed uncertainty quantification methodology based on pseudo marginal likelihood and…

In this paper, we develop a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of the two-fluid model-based multiphase computational fluid dynamics (MCFD) for bubbly flow simulations. The proposed…

Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…

In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…

We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chernov and Le (2024) as well as Harbrecht, Schmidlin, and Schwab…

There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of…

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…

Accurately simulating coupled physical processes under uncertainty is essential for reliable modeling and design in performance-critical applications such as combustion systems. Ablative heat shield design, as a specific example of this…

Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here…

This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…