Generative Network for Schroedinger Equation

Abstract

Schrodinger equation is a linear partial differential equation that describes the behavior or change of quantum systems. Recent machine learning approaches solve this equation by searching for the optimal neural networks representing the wave functions that minimize the system energy. Since the exact energy calculation requires integral evaluation, those approaches use the Markov Chain Monte Carlo (MCMC) for estimating the integral. In this paper we follow a different strategy to solve the Schroedinger equation, instead of modeling the wave functions as neural networks, we directly model the generative process that generates electron coordinates. This enables us to estimate the integral using the random samples from the generative networks in parallel, thus it is more efficient than the MCMC-based approach which is a sequential random sampling method. Experiments results show that our method produces promising solutions to the Schrodinger equation. We also discuss the limitation and the promise of the proposed approach compared to the state of the art results. The source code is open-sourced.