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Article

Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential

1
Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
2
Department of ICT, Virovitica College, 33000 Virovitica, Croatia
*
Author to whom correspondence should be addressed.
Entropy 2021, 23(1), 95; https://doi.org/10.3390/e23010095
Received: 29 November 2020 / Revised: 7 January 2021 / Accepted: 8 January 2021 / Published: 11 January 2021
(This article belongs to the Special Issue Human-Centric AI: The Symbiosis of Human and Artificial Intelligence)
We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm. View Full-Text
Keywords: Anderson localization; deep neural networks; residual error estimates; physics informed neural networks Anderson localization; deep neural networks; residual error estimates; physics informed neural networks
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MDPI and ACS Style

Grubišić, L.; Hajba, M.; Lacmanović, D. Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential. Entropy 2021, 23, 95. https://doi.org/10.3390/e23010095

AMA Style

Grubišić L, Hajba M, Lacmanović D. Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential. Entropy. 2021; 23(1):95. https://doi.org/10.3390/e23010095

Chicago/Turabian Style

Grubišić, Luka, Marko Hajba, and Domagoj Lacmanović. 2021. "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential" Entropy 23, no. 1: 95. https://doi.org/10.3390/e23010095

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