Plasmonic hydrogen gas sensors have become widely used in recent years due to their low cost, reliability, safety, and measurement accuracy. In this paper, we designed, optimized, and fabricated a palladium (Pd)-coated nano-grating-based plasmonic hydrogen gas sensor; and investigated using the finite-difference time-domain method and experimental spectral reflectance measurements, the calibrated effects of hydrogen gas exposure on the mechano-optical properties of the Pd sensing layer. The nanostructures were fabricated using DC sputter deposition onto a one-dimensional nano-grating optimized with a thin-film gold buffer to extend the optical response dynamic range and performance stability; the color change sensitivity of the Pd surface layer was demonstrated for hydrogen gas concentrations as low as 0.5 vol.%, up to 4 vol.%, based on the resonance wavelength shift within the visible band corresponding to the reversible phase transformation. Visual color change detection of even the smallest hydrogen concentrations indicated the high sensitivity of the gas sensor. Our technique has potential for application to high-accuracy portable plasmonic sensors compatible with biochemical sensing with smartphones.

A lot of machine learning algorithms, including clustering methods such as K-nearest neighbor (KNN), highly depend on the distance metrics to understand the data pattern well and to make the right decision based on the data. In recent years, studies show that distance metrics can significantly improve the performance of the machine learning or deep learning model in clustering, classification, data recovery tasks, etc. In this article, we provide a survey on widely used distance metrics and the challenges associated with this field. The most current studies conducted in this area are commonly influenced by Siamese and triplet networks utilized to make associations between samples while employing mutual weights in deep metric learning (DML). They are successful because of their ability to recognize the relationships among samples that show a similarity. Furthermore, the sampling strategy, suitable distance metric, and network structure are complex and difficult factors for researchers to improve network model performance. So, this article is significant because it is the most recent detailed survey in which these components are comprehensively examined and valued as a whole, evidenced by assessing the numerical findings of the techniques.

It is often said that mathematical modeling is an implementation of mathematics in real-world problems with the aim of better understanding them, so we can say that mathematical modeling is linked to the solution of problems. Some of the essential principles and procedures of mathematical modeling are discussed using formulas and equations. We investigate the stability and convergence characteristics and demonstrate the suitability of different mathematical methods in a set of numerical examples. The described methods in our paper are the best choices for the simulation of linear phenomena and are more efficient for use with high-order spatial discretization. We emphasized the importance of mathematical modeling technologies used in computational tools. Our study shows that these new methods are more stable with lower errors.