Classification of nodal pockets in many-electron wave functions via machine learning

Abstract

Accurate treatment of electron correlation in quantum chemistry requires solving the many-electron problem. If the nodal surface of a many-electron wave function is available even in an approximate form, the fixed-node diffusion Monte Carlo (FNDMC) approach from the family of quantum Monte Carlo methods can be successfully used for this purpose. The issue of description and classification of nodal surfaces of fermionic wave functions becomes central for understanding the basic properties of many-electron wave functions and for the control of accuracy and computational efficiency of FNDMC computations. In this work, we approach the problem of automatic classification of nodal pockets of many-electron wave functions. We formulate this problem as that of binary classification and apply a number of techniques from the machine learning literature. We apply these techniques on a range of atoms of light elements and demonstrate varying degrees of success. We observe that classifiers with relatively simple geometry perform poorly on the classification task; methods based on a random collection of tree-based classifiers appear to perform best. We conclude with thoughts on computational challenges and complexity associated with applying these techniques to heavier atoms.