Machine Learning of Two-Electron Reduced Density Matrices for Many-Body Problems

We present a novel machine learning algorithm for the many-electron problem, predicting the convex combination of two-electron reduced density matrices (2-RDMs)─obtained from upper- and lower-bound energy calculations─that closely approximates the exact energy. In contrast to other recently developed approaches based on the wave function or one-electron density, our 2-RDM machine-learning approach predicts energies and properties without steep scaling or functional approximation. As conjectured by Preskill and co-workers, a small amount of data in a physics-based machine learning algorithm─in this case, information about the RDMs and their violation of selected higher-order <i>N</i>-representability conditions─yields highly accurate electronic energies that capture both dynamic and static correlation. We demonstrate the method by predicting the potential energy curves for BH and N₂ within a few millihartrees of results from exact diagonalization. This machine learning algorithm provides a general framework for improving electronic structure calculations, with the potential for wide-reaching applications to both moderately and strongly correlated molecular systems.