# Deep learning and the Schr"odinger equation

arXiv: https://arxiv.org/abs/1702.01361 · HTML: https://mlsanity.com/paper/1702.01361/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2017.

## Built on by (most cited first, 5 of 5)

- [A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate](https://mlsanity.com/paper/2102.02617/) (2021)
- [Bridging the reality gap in quantum devices with physics-aware machine learning](https://mlsanity.com/paper/2111.11285/) (2021)
- [Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery](https://mlsanity.com/paper/2205.02967/) (2022)
- [Hermite Neural Network Simulation for Solving the 2D Schrodinger Equation](https://mlsanity.com/paper/2402.10649/) (2024)
- [Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalization](https://mlsanity.com/paper/2505.18288/) (2025)

## Abstract (arXiv)

We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the neural network model was able to predict the ground-state energy to within chemical accuracy, with a median absolute error of 1.49 mHa. We also investigate the performance of the model in predicting other quantities such as the kinetic energy and the first excited-state energy of random potentials.