Related papers: Uncertainty Quantification in Forward Problems: Ba…
In this article, we develop a set-oriented numerical methodology which allows to perform uncertainty quantification (UQ) for dynamical systems from a global point of view. That is, for systems with uncertain parameters we approximate the…
This study presents a comprehensive framework for uncertainty quantification (UQ) and design optimization of plasma etching in semiconductor manufacturing. The framework is demonstrated using experimental measurements of etched depth…
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…
In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping,…
We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…
We study a chemical kinetic system with uncertainty modeling a gene regulatory network in biology. Specifically, we consider a system of two equations for the messenger RNA and micro RNA content of a cell. Our target is to provide a simple…
Deep learning-based object pose estimators are often unreliable and overconfident especially when the input image is outside the training domain, for instance, with sim2real transfer. Efficient and robust uncertainty quantification (UQ) in…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
In this article, we propose a modified convex combination of the polynomial reconstructions of odd-order WENO schemes to maintain the central substencil prevalence over the lateral ones in all parts of the solution. New "centered" versions…
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…
Deploying deep neural networks on resource-constrained devices faces two critical challenges: maintaining accuracy under aggressive quantization while ensuring predictable inference latency. We present a curiosity-driven quantized…
We present a "module-based hybrid" Uncertainty Quantification (UQ) framework for general nonlinear multi-physics simulation. The proposed methodology, introduced in [\hyperlink{ref1}{1}], supports the independent development of each…
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…
Calibration is crucial in deep learning applications, especially in fields like healthcare and autonomous driving, where accurate confidence estimates are vital for decision-making. However, deep neural networks often suffer from…
This paper develops a robust control synthesis method for uncertain linear systems with input saturation in the framework of integral quadratic constraints (IQCs). The system is reformulated as a linear fractional representation (LFR) that…
Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
Machine-learned potentials (MLPs) have revolutionized materials discovery by providing accurate and efficient predictions of molecular and material properties. Graph Neural Networks (GNNs) have emerged as a state-of-the-art approach due to…
Neural networks (NNs) often assign high confidence to their predictions, even for points far out-of-distribution, making uncertainty quantification (UQ) a challenge. When they are employed to model interatomic potentials in materials…
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…