Physics-informed Reduced-Order Learning from the First Principles for Simulation of Quantum Nanostructures

TL;DR

This paper introduces a physics-informed reduced-order learning approach for simulating the Schrödinger equation in quantum nanostructures, significantly reducing computational costs while maintaining high accuracy and generalization to untrained conditions.

Contribution

It presents a novel physics-informed learning algorithm that drastically reduces degrees of freedom and computational time for quantum simulations based on first principles.

Findings

Over 3 orders of magnitude reduction in DoF

2 orders of magnitude reduction in computational time

Accurate predictions beyond training conditions

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.