Related papers: An efficient epistemic uncertainty quantification …
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
We analyze an ensemble-based approach for uncertainty quantification (UQ) in atomistic neural networks. This method generates an epistemic uncertainty signal without requiring changes to the underlying multi-headed regression neural network…
We present a novel uncertainty quantification approach for high-dimensional stochastic partial differential equations that reduces the computational cost of polynomial chaos methods by decomposing the computational domain into…
The design of next-generation alloys through the Integrated Computational Materials Engineering (ICME) approach relies on multi-scale computer simulations to provide thermodynamic properties when experiments are difficult to conduct.…
The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and…
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…
Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…
Uncertainty Quantification (UQ) is a promising approach to improve model reliability, yet quantifying the uncertainty of Large Language Models (LLMs) is non-trivial. In this work, we establish a connection between the uncertainty of LLMs…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions,…
Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…
In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…
The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use…
A model's ability to express its own predictive uncertainty is an essential attribute for maintaining clinical user confidence as computational biomarkers are deployed into real-world medical settings. In the domain of cancer digital…