Related papers: Uncertainty quantification for complex systems wit…
Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…
Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate very…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient…
The introduction of the Segment Anything Model (SAM) has paved the way for numerous semantic segmentation applications. For several tasks, quantifying the uncertainty of SAM is of particular interest. However, the ambiguous nature of the…
Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work…
This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…
In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically…
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…
Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents…
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…
Recent investigations have emphasized the importance of uncertainty quantification (UQ) to describe errors in nuclear theory. We carry out UQ for configuration-interaction shell model calculations in the $1s$-$0d$ valence space,…
With the advancement of GPS, remote sensing, and computational simulations, large amounts of geospatial and spatiotemporal data are being collected at an increasing speed. Such emerging spatiotemporal big data assets, together with the…
On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and…
Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…
We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN),…
Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an…