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As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…

This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect…

The goals of this chapter are twofold. First, we wish to introduce molecular dynamics (MD) and uncertainty quantification (UQ) in a common setting in order to demonstrate how the latter can increase confidence in the former. In some cases,…

Large Language Models (LLMs) are commonly used in Question Answering (QA) settings, increasingly in the natural sciences if not science at large. Reliable Uncertainty Quantification (UQ) is critical for the trustworthy uptake of generated…

Reliable uncertainty quantification (UQ) is essential for ensuring trustworthy downstream use of large language models, especially when they are deployed in decision-support and other knowledge-intensive applications. Model certainty can be…

Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured…

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as…

The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40<A<100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure…

Understanding how specific components of the nuclear interaction shape observable properties of atomic nuclei remains a central challenge in nuclear structure research. While previous studies have focused on bulk observables such as nuclear…

The nuclear shell model is one of the successful models in theoretical understanding of nuclear structure. If a convenient effective interaction can be found between nucleons, various observables such as energies of nuclear states are…

Predicting fuel assembly bow in pressurized water reactors requires solving tightly coupled fluid-structure interaction problems, whose direct simulations can be computationally prohibitive, making large-scale uncertainty quantification…

We review the status and prospects of theoretical studies of neutrino-nucleus interactions, and discuss the influence of the treatment of nuclear effects on the determination of oscillation parameters. The models developed to describe the…

The value of uncertainty quantification on predictions for trained neural networks (NNs) on quantum chemical reference data is quantitatively explored. For this, the architecture of the PhysNet NN was suitably modified and the resulting…

Heisenberg uncertainty principle describes a basic restriction on observer's ability of precisely predicting the measurement for a pair of non-commuting observables, and virtually is at the core of quantum mechanics. We herein aim to study…

Large Language Models (LLMs) are increasingly assisting users in the real world, yet their reliability remains a concern. Uncertainty quantification (UQ) has been heralded as a tool to enhance human-LLM collaboration by enabling users to…

For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

The High Temperature Reactor Code Package provides sophisticated modeling and simulation capabilities for high temperature gas cooled reactors like the HTR-200 Modul. However, HCP currently lacks integrated methods for uncertainty…

Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been under-explored. To address this, we have used…

Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of…