Physics-informed Reduced-Order Learning from the First Principles for
Simulation of Quantum Nanostructures
- URL: http://arxiv.org/abs/2302.00100v2
- Date: Sat, 15 Apr 2023 14:53:24 GMT
- Title: Physics-informed Reduced-Order Learning from the First Principles for
Simulation of Quantum Nanostructures
- Authors: Martin Veresko and Ming-Cheng Cheng
- Abstract summary: In large-scale nanostructures, extensive computational effort may become prohibitive due to the high degrees of freedom (DoF)
This study employs a reduced-order learning algorithm, enabled by the first principles, for simulation of the Schr"odinger equation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger
equation is needed for design and analysis of quantum nanostructures that offer
numerous applications in biology, medicine, materials, electronic/photonic
devices, etc. In large-scale nanostructures, extensive computational effort
needed in DNS may become prohibitive due to the high degrees of freedom (DoF).
This study employs a reduced-order learning algorithm, enabled by the first
principles, for simulation of the Schr\"odinger equation to achieve high
accuracy and efficiency. The proposed simulation methodology is applied to
investigate two quantum-dot structures; one operates under external electric
field, and the other is influenced by internal potential variation with
periodic boundary conditions. The former is similar to typical operations of
nanoelectronic devices, and the latter is of interest to simulation and design
of nanostructures and materials, such as applications of density functional
theory. Using the proposed methodology, a very accurate prediction can be
realized with a reduction in the DoF by more than 3 orders of magnitude and in
the computational time by 2 orders, compared to DNS. The proposed
physics-informed learning methodology is also able to offer an accurate
prediction beyond the training conditions, including higher external field and
larger internal potential in untrained quantum states.
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