Related papers: Old but Not Obsolete: Dimensional Analysis in Nond…
In this paper we present an advanced numerical method to simulate a real life challenging industrial problem that consists of the non-destructive testing in steam generators. We develop a finite element technique that handles the big data…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…
Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional…
In the present study, a new set of dimensionless coefficients is introduced through non-dimensionalization of electrochemical equations of lead-acid batteries. Non-dimensionalization process has been applied to the electrochemical governing…
Self-sensing conductive composites can reveal deformation and damage through measurable changes in electrical resistance, which makes them attractive for embedded diagnostics and learning-enabled structural health monitoring. This paper…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
An electrical impedance spectroscopy-based nondestructive testing (NDT) method is proposed to image both cracks and reinforcing bars in concrete structures. The method utilizes the frequency-dependent behavior of thin insulating cracks:…
Classical dimensional analysis has two limitations: (i) the computed dimensionless groups are not unique, and (ii) the analysis does not measure relative importance of the dimensionless groups. We propose two algorithms for estimating…
We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity:…
Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…
The identification of new rare signals in data, the detection of a sudden change in a trend, and the selection of competing models, are among the most challenging problems in statistical practice. These challenges can be tackled using a…
The development and first applications of a new periodic energy decomposition analysis (pEDA) scheme for extended systems based on the Kohn-Sham approach to density functional theory are described. The pEDA decomposes the binding energy…
This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…
We introduce a new parameterization of $B\rightarrow D \pi \ell \nu$ form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…