Related papers: Analytical Identification of Design and Multidimen…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
This paper compares the parametric design space with a feature space generated by the extraction of design features using deep learning (DL) as an alternative way for design space exploration. In this comparison, the parametric design space…
Software development in the aerospace domain requires adhering to strict, high-quality standards. While there exist regulatory guidelines for commercial software in this domain (e.g., ARP-4754 and DO-178), these do not apply to software…
It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
Assessing predictive models can be challenging. Modelers must navigate a wide array of evaluation methodologies implemented with incompatible interfaces across multiple packages which may give different or even contradictory results, while…
In this paper, we present Sinkhorn multidimensional scaling (Sinkhorn MDS) as a method for visualizing shape functionals in shape spaces. This approach uses the Sinkhorn divergence to map these infinite-dimensional spaces into…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
The term "Active Plasma Resonance Spectroscopy" refers to a class of diagnostic methods which employ the ability of plasmas to resonate on or near the plasma frequency. The basic idea dates back to the early days of discharge physics: An…
Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations (DFAs) are published every year. To become available in program packages, the novel DFAs need to be (re)implemented.…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
RSDs (Resistive AC-Coupled Silicon Detectors) are n-in-p silicon sensors based on the LGAD (Low-Gain Avalanche Diode) technology, featuring a continuous gain layer over the whole sensor area. The truly innovative feature of these sensors is…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
Environment perception is a fundamental part of the dynamic driving task executed by Autonomous Driving Systems (ADS). Artificial Intelligence (AI)-based approaches have prevailed over classical techniques for realizing the environment…