Emergent Schrödinger equation in an introspective machine learning architecture

Ce Wang; Hui Zhai; Yi-Zhuang You

doi:10.1016/j.scib.2019.07.014

Emergent Schrödinger equation in an introspective machine learning architecture

Sci Bull (Beijing). 2019 Sep 15;64(17):1228-1233. doi: 10.1016/j.scib.2019.07.014. Epub 2019 Jul 22.

Authors

Ce Wang¹, Hui Zhai², Yi-Zhuang You³

Affiliations

¹ Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
² Institute for Advanced Study, Tsinghua University, Beijing 100084, China. Electronic address: hzhai@tsinghua.edu.cn.
³ Department of Physics, University of California, San Diego, CA 92093, USA. Electronic address: yzyou@physics.ucsd.edu.

PMID: 36659603
DOI: 10.1016/j.scib.2019.07.014

Abstract

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schrödinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schrödinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.

Keywords: Machine learning; Neural network; Potential-to-density mapping; Quantum physics; Recurrent autoencoder.