Solving the Schro?dinger Equation in the Configuration Space with Generative Machine Learning

The configuration interaction approach provides a concep-tually simple and powerful approach to solve the Schro''dinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.

Automated summary

The configuration interaction approach is a powerful method for solving the Schrödinger equation in realistic molecules and materials, but it has a scalability issue that limits its practical use. In this study, we propose a machine learning approach to selectively generate important configurations, which leads to faster convergence to chemical accuracy compared to random sampling or Monte Carlo configuration interaction method. This work opens up new possibilities for using generative models to solve electronic structure problems.