85. Neural Network Models for Eigenvalue Problems
Invited abstract in session WC-4: Large scale optimization and applications 1 , stream Large scale optimization and applications.
Wednesday, 10:00 - 11:30Room: C105
Authors (first author is the speaker)
| 1. | Marko Hajba
|
| Department of ICT, Virovitica University of Applied Sciences | |
| 2. | Luka Grubisic
|
Abstract
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. Our computational model is posed in the truncated finite domain, and this is an approximation of
the standard Schrödinger Hamiltonian. Our chosen task is to compute localized bounded states at the lower end of the spectrum. Neural networks (NNs) are used as surrogate models which represent dependence of the ground state or landscape function on the localizing potential, depending on a problem we are solving. Further, we will also demonstrate the use of Variational Physics Informed Neural Network, together with the residual type error estimates, to obtain the ground state of the eigenvalue problem. Error estimators will be introduced to monitor the performance of the model. We present a host of numerical experiments to benchmark the accuracy and performance of the proposed algorithms.
Keywords
- Artificial intelligence based optimization methods and appl
Status: accepted
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