# Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling

arXiv: https://arxiv.org/abs/2106.03126 · HTML: https://mlsanity.com/paper/2106.03126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 6 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Learning Potentials of Quantum Systems using Deep Neural Networks](https://mlsanity.com/paper/2006.13297/) (2020)
- [QFold: Quantum Walks and Deep Learning to Solve Protein Folding](https://mlsanity.com/paper/2101.10279/) (2021)

## Built on by (most cited first, 1 of 1)

- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)

## Abstract (arXiv)

The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which we dub as Metropolis potential neural network (MPNN). A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation. Benchmarking on the harmonic oscillator and hydrogen atom, MPNN shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrodinger equation, but also the eigen-energy. Our proposal could be potentially applied to the ab-initio simulations, and to inversely solving other partial differential equations in physics and beyond.