https://doi.org/10.1140/epjp/s13360-025-06381-2
Regular Article
Theoretical modeling and AI-driven approximation of energy spectrum behavior in nano-engineered films
1
Department of Electrical & Computer Engineering, COMSATS University Islamabad, G.T. Road, 47040, Wah Cantonment, Pakistan
2
Department of Information Systems, College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia
3
Department of Computer Science, Tulane University, 6823 St. Charles Ave., 70118, New Orleans, LA, USA
4
Division of Physical and Natural Sciences, School of Arts and Sciences, University of The Gambia, Serrekunda, Gambia
5
Department of Mathematics, COMSATS University Islamabad, G.T. Road, 47040, Wah Cantonment, Pakistan
Received:
3
October
2024
Accepted:
29
April
2025
Published online:
30
May
2025
We propose a method for disclosing properties of the Hofstadter butterfly by exploiting the analogy of Bloch electrons in a superconducting thin film with periodic hole arrays and an applied magnetic field. We show that various properties, including the magneto-resistance effect of the Hofstadter butterfly, may be observed in carefully selected conditions, such as diameter and distance between two holes. Additionally, we advise employing approximation methods to infer the magneto-resistance properties rather than persistently measuring them, and we present an entire framework for this purpose. The latter solves difficult and nonlinear issues using a machine learning method known as the group method of data handling-type neural networks. The simulation results of our model show excellent approximations for the mean-squared error values.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
