This repository contains some of the experiments and additional materials for a research paper Deep neural network model for approximating eigenmodes localized by a confining potential which is accepted to the open-access journal Entropy. Authors: Luka Grubišić, Marko Hajba, Domagoj Lacmanović
The research paper is accepted as a part of the special issue "Human-Centric AI: The Symbiosis of Human and Artificial Intelligence" and it is freely available at: https://www.mdpi.com/journal/entropy/special_issues/Human-Centric_AI
Direct link to the paper: https://www.mdpi.com/1099-4300/23/1/95
If you find this codes or paper usefull in your research, please cite (the are other styles available on the links above):
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.
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.
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.
You can expect to find code, data and some of the results inside folders. There are more details inside corresponding .ipynb files.
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Ground_state_VPINN_1D folder contains jupyter notebook, data and some of the additional results for the problem of calculating the ground state of the Schrödinger equation in 1 dimension using a Certified Deep Ritz method.
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Landscape_function_VPINN_2D folder contains jupyter notebook, data and some of the additional results for the problem of calculating landscape function as a solution of the equation
Tensorflow 2
Keras
FEniCS
NumPy
SciPy
Matplotlib