Optimizing machine learning electronic structure methods based on the one-electron reduced density matrix

Regression methods can be employed to "learn" the electronic structure of molecules and materials, e.g. by learning the electron density [1] [2], the spectral density [3], or the one-body reduced density matrix (1-rdm) [4]. We present a comprehensive analysis of the regression model used for learning the map linking the external potential to the 1-rdm. We span kernel ridge regressions (KRR), as well as deep learning utilizing a common set of training data. We employ cross-validation techniques to refine hyper-parameters of each KRR model. We find that KRR with an optimized RBF kernel (a Gaussian kernel) generally outperforms other models and provides us with 1-rdms that do not require secondary learning steps to reach self-consistent field quality. Our work extends the applicability and robustness of the current state-of-the-art models [4].