Related papers: Hierarchical multiscale quantification of material…

Ensuring structural reliability remains a core concern in civil engineering, yet the quantitative effects of quality control measures on material variability and safety margins are not fully understood, especially for materials other than…

This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…

Smart matter consists of many sensors, computers and actuators embedded within materials. These microelectromechanical systems allow properties of the materials to be adjusted under program control. In this context, we study the behavior of…

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

Hierarchical microstructures are often invoked to explain the high resilience and fracture toughness of biological materials such as bone and nacre. Biomimetic material models inspired by those structural arrangements face the obvious…

Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Trust is a crucial factor affecting the adoption of machine learning (ML) models. Qualitative studies have revealed that end-users, particularly in the medical domain, need models that can express their uncertainty in decision-making…

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional…

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Materials informatics is increasingly used to support modelling, analysis and design across the length scales of materials science, from atomistic simulations to microstructural characterisation and continuum descriptions. Despite rapid…

While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources…

We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model. We do so in an adaptive setting without assuming knowledge of the sparsity level (number of…

Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are…