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

Abstract

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.

Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

“…In a study by da Silva Macedo et al an NN was trained to predict the energy levels and energy-dependent masses as nonparabolic properties of semiconductor heterostructures [34]. The learning ability of a physics-informed proper orthogonal decomposition-Galerkin simulation methodology for QD structures was investigated by Veresko and Cheng [35]. In a recently published paper, we used two different neural architectures to approach 1-D SE in quantum wells (QWs) with arbitrary CPs [36].…”