confinement dimensionality
Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures
Kozoň, Marek, Schrijver, Rutger, Schlottbom, Matthias, van der Vegt, Jaap J. W., Vos, Willem L.
Abstract: We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering. 1. Introduction Completely controlling wave propagation in periodic media is a key challenge that is essential for a large variety of applications [2-16]. An especially interesting type of control is wave confinement achieved by introducing disorder and functional defects into an otherwise periodic medium [17-20]. The interference of waves in such an altered structure may result in a strong concentration of the energy density inside a small sub-volume of the medium. Wave confinement has been investigated for different types of waves and in various settings, e.g., classical mechanics [21], photonics [10, 11, 22-24], solid state physics [25-29], or magnonics [30, 31]. Its applications include sensors, controlled spontaneous emission, and enhanced interactions between hybrid wave-types such as sound and light [32-40].