From expNN to sinNN: automatic generation of sum-of-products models for potential energy surfaces in internal coordinates using neural networks and sparse grid sampling

Abstract: Potential Energy Surfaces are generally required for simulating quantum dynamics. Specifically, having an analytical expression of the PES enables a more efficient dynamics workflow compared to the currently popular direct dynamics approaches. When using the MCTDH method, there is also a strong advantage to express the PES in sum-of-products form for solving the time-dependent nuclear Schr\"odinger equation. Nevertheless, obtaining an accurate expression for the PES of molecular systems that contain more than a few atoms presents challenges. The objectives of this work are twofold. First, the practicality of a single-layer artificial neural network with sinusoidal activation functions for representing potential energy surfaces in sum-of-products form will be evaluated. Second, the efficiency and ability of a homogeneous sampling strategy based on sparse grids to provide unbiased coverage of configuration space for generating training data will be assessed. The fitting approach, named sinNN, is applied to modeling the PES of HONO, covering both the trans and cis isomers. Refitting is first explored with comparison to the expNN fitting method. Second, fitting from potential energies obtained from the machine learning model MLatom/AIQM2 is considered. The sinNN PES model obtained from MLatom/AIQM2 energies was able to reproduce available experimental fundamental vibrational transition energies with a root mean square error of about 17 cm-1. sinNN combined with sparse grids sampling approach proves to be of practical use for the chosen system, both at refitting and direct fitting tasks. The ability of MLatom/AIQM models to accurately reproduce global PESs beyond equilibrium geometries is of particular interest.