Dual-Level Parametrically Managed Neural Network Method for Learning a Potential Energy Surface for Efficient Dynamics

A general difficulty with machine-learned potential energy surfaces is their unreliability in regions with little or no training data. The goal of the present work is to remedy this by a low-cost method for incorporating well understood features of potential energy surfaces into an efficient data-driven machine learning algorithm. Our focus is on regions where conventional surface fitting does not need large amounts of accurate data, in particular, geometries with large separations of subsystems-where it is well recognized that the potential should reach its asymptotic form-and geometries with very close atoms-where the potential should be repulsive enough to prevent trajectories from reaching classically inaccessible regions but need not be highly quantitative. The new method involves a neural network (NN) with a parametrically managed activation function (PMAF) and two levels of electronic structure, a higher level (HL) and a lower level (LL). The resulting NN is called a dual-level parametrically managed neural network (DL-PMNN). For the present example, the HL is an accurate density functional method (CF22D/may-cc-pVTZ), and the LL is an inexpensive density functional method (MPW1K/MIDIY). We use the LL to ensure correct behavior of the potential at large and small distances; the goal is to reach HL accuracy for dynamics without making HL calculations in regions where the LL can guide the fit. To illustrate the new method, we fit the potential energy surface for dissociation of the S-H bond of <i>ortho</i>-fluorothiophenol in the ground electronic state, and we show that the method yields a good fit and efficient trajectory calculations without crashes.