Physics-informed Reduced-Order Learning from the First Principles for Simulation of Quantum Nanostructures
This addresses the prohibitive computational effort in multi-dimensional simulations for quantum nanostructures, with applications in fields like biology and electronics, though it appears incremental as it builds on existing reduced-order methods.
The study tackled the high computational cost of simulating the Schrödinger equation for quantum nanostructures by developing a physics-informed reduced-order learning algorithm, achieving a reduction in degrees of freedom by over 3 orders of magnitude and computational time by 2 orders while maintaining high accuracy.
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 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. 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.