Related papers: Uncertainty Quantification of Phase Transition Pro…
We use the quantum Brownian model to derive the uncertainty relation for a quantum open system in an arbitrarily-squeezed initial state interacting with an environment at finite temperature. We examine the relative importance of the quantum…
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary…
Trustworthy deployment of ML models requires a proper measure of uncertainty, especially in safety-critical applications. We focus on uncertainty quantification (UQ) for classification problems via two avenues -- prediction sets using…
We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number,…
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 this work, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann…
Quantifying uncertainties for machine learning models is a critical step to reduce human verification effort by detecting predictions with low confidence. This paper proposes a method for uncertainty quantification (UQ) of table structure…
TodevelopanovelUncertaintyQuantification (UQ) framework to estimate the uncertainty of patient survival models in the absence of ground truth, we developed and evaluated our approach based on a dataset of 1383 patients treated with…
The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties,…
We are concerned with the nonlinear problem $u_t=u_{xx}+f(u)$, where $f$ is of combustion type, coupled with the Stefan-type free boundary $h(t)$. According to [4,5], for some critical initial data, the transition solution $u$ locally…
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…
Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A…
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective…
The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such…
High-dimensional tensor data often exhibit strong temporal correlations that appear as low-dimensional structures in the frequency domain. While the low-tubal-rank tensor model effectively captures these spectral features, making it…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a…
The uncertainty principle guarantees a non-zero value for the positional uncertainty, $\left\langle \Delta x^2\right\rangle > 0$, even without thermal fluctuations. This implies that quantum fluctuations inherently enhance positional…