TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.4.3.022
TI  - Predicting quantum potentials by deep neural network and metropolis sampling
PY  - 2021/09/13
UR  - https://www.scipost.org/SciPostPhysCore.4.3.022
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 4
IS  - 3
SP  - 022
A1  - Hong, Rui
AU  - Zhou, Peng-Fei
AU  - Xi, Bin
AU  - Hu, Jie
AU  - Ji, An-Chun
AU  - Ran, Shi-Ju
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.4.3.022,
	title={{Predicting quantum potentials by deep neural network and metropolis sampling}},
	author={Rui Hong and Peng-Fei Zhou and Bin Xi and Jie Hu and An-Chun Ji and Shi-Ju Ran},
	journal={SciPost Phys. Core},
	volume={4},
	pages={022},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.4.3.022},
	url={https://scipost.org/10.21468/SciPostPhysCore.4.3.022},
}