An Effective Simulation Methodology of Quantum Nanostructures based on Model Order Reduction

Veresko, Martin; Cheng, Ming-Cheng

doi:10.1109/sispad54002.2021.9592599

Cited by 2 publications

(2 citation statements)

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“…The physics-informed POD-Galerkin simulation methodology based on the global quantum POD model 50 has been applied to investigate its learning ability for simulations of two QD structures, one influenced by external electric field and the other by internal potential and BCs. The extraordinary learning ability of the POD-Galerkin methodology has been demonstrated even in the untrained states subjected to applied field and internal potential beyond the training conditions.…”

Section: Discussionmentioning

confidence: 99%

“…1b vary very little, which reveals that the first 6 POD modes tend to maximize the information on all the 6 selected trained QSs. This is because the global quantum POD approach 50 implemented in this study generates POD modes that represent WFs in all N Q selected QSs, where N Q = 6 in this case. Apparently, the most essential LS information is captured by the first N Q POD modes, and thus the eigenvalue decreases sharply beyond the N Q -th mode.…”

Section: Demonstrationsmentioning

confidence: 99%

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Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

Veresko

Cheng

2023

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Multi-dimensional direct numerical simulation (DNS) of the Schrödinger 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 physics-based reduced-order learning algorithm, enabled by the first principles, for simulation of the Schrödinger 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. In each structure, cases within and beyond training conditions are examined. 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. An accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states, is also achieved. Comparison is also carried out between the physics-based learning and Fourier-based plane-wave approaches for a periodic case.

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Section: Discussionmentioning

confidence: 99%

Section: Demonstrationsmentioning

confidence: 99%