# Deep learning extraction of band structure parameters from density of states: a case study on trilayer graphene

arXiv: https://arxiv.org/abs/2210.06310 · HTML: https://mlsanity.com/paper/2210.06310/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)

## Built on by (most cited first, 2 of 2)

- [Invariant multiscale neural networks for data-scarce scientific applications](https://mlsanity.com/paper/2406.08318/) (2024)
- [Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction](https://mlsanity.com/paper/2508.10718/) (2025)

## Abstract (arXiv)

The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.