Structure-based Sampling and Self-correcting Machine Learning for Accurate Calculations of Potential Energy Surfaces and Vibrational Levels

Abstract

We present an efficient approach for generating highly accurate molecular potential energy surfaces (PESs) using self-correcting, kernel ridge regression (KRR) based machine learning (ML). We introduce structure-based sampling to automatically assign nuclear configurations from a pre-defined grid to the training and prediction sets, respectively. Accurate high-level \textit{ab initio} energies are required only for the points in the training set, while the energies for the remaining points are provided by the ML model with negligible computational cost. The proposed sampling procedure is shown to be superior to random sampling and also eliminates the need for training several ML models. Self-correcting machine learning has been implemented such that each additional layer corrects errors from the previous layer. The performance of our approach is demonstrated in a case study on a published high-level \textit{ab initio} PES of methyl chloride with 44,819 points. The ML model is trained on sets of different size and then used to predict the energies for tens of thousands of nuclear configurations within seconds. The resulting datasets are utilized in variational calculations of the vibrational energy levels of CH$_3$Cl. By using both structure-based sampling and self-correction, the size of the training set can be kept small (e.g. 10\% of the points) without any significant loss of accuracy. In \textit{ab initio} rovibrational spectroscopy, it is thus possible to reduce the number of computationally costly electronic structure calculations through structure-based sampling and self-correcting KKR-based machine learning by up to 90\%.