基于第一性原理的物理信息降阶学习用于量子纳米结构模拟
Physics-informed Reduced-Order Learning from the First Principles for Simulation of Quantum Nanostructures
AI总结：
本文提出由第一性原理赋能的物理信息降阶学习方法，用于高效模拟 Schrödinger 方程，并在两类量子点结构中以更低自由度和计算成本实现高精度及训练外预测。
摘要：
量子纳米结构在生物学、医学、材料、电子/光子器件等领域具有众多应用，其设计与分析需要对 Schrödinger 方程进行多维直接数值模拟（DNS）。在大规模纳米结构中，由于自由度（DoF）很高，DNS 所需的巨大计算量可能令人难以承受。本研究采用一种由第一性原理赋能的降阶学习算法来模拟 Schrödinger 方程，以实现高精度和高效率。所提出的模拟方法被用于研究两种量子点结构：一种在外部电场下工作，另一种则在周期边界条件下受内部势变化影响。前者类似于纳米电子器件的典型工作方式，后者则与纳米结构和材料的模拟及设计相关，例如密度泛函理论应用。使用所提出的方法，可以实现非常准确的预测；与 DNS 相比，其 DoF 降低超过 3 个数量级，计算时间降低 2 个数量级。所提出的物理信息学习方法还能够在训练条件之外提供准确预测，包括在未经训练的量子态中面对更高外场和更大内部势的情形。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
