Active learning of many-body configuration space: Application to the Cs+-water MB-nrg potential energy function as a case study

The efficient selection of representative configurations that are used in high-level electronic structure calculations needed for the development of many-body molecular models poses a challenge to current data-driven approaches to molecular simulations. Here, we introduce an active learning (AL) framework for generating training sets corresponding to individual many-body contributions to the energy of an N-body system, which are required for the development of MB-nrg potential energy functions (PEFs). Our AL framework is based on uncertainty and error estimation and uses Gaussian process regression to identify the most relevant configurations that are needed for an accurate representation of the energy landscape of the molecular system under examination. Taking the Cs+-water system as a case study, we demonstrate that the application of our AL framework results in significantly smaller training sets than previously used in the development of the original MB-nrg PEF, without loss of accuracy. Considering the computational cost associated with high-level electronic structure calculations, our AL framework is particularly well-suited to the development of many-body PEFs, with chemical and spectroscopic accuracy, for molecular-level computer simulations from the gas to the condensed phase.