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

arXiv: https://arxiv.org/abs/2302.00100 · HTML: https://mlsanity.com/paper/2302.00100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 58 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 2 of 2)

- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [A Methodology for Thermal Simulation of Interconnects Enabled by Model Reduction with Material Property Variation](https://mlsanity.com/paper/2112.03023/) (2021)

## Abstract (arXiv)

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.