Machine learning of atomic forces from quantum mechanics: An approach based on pairwise interatomic forces

In this work, we explore a machine learning approach based on pairwise interatomic forces to directly predict atomic forces in a molecule to quantum chemical accuracy. The scheme, denoted pairF-Net, uses a neural network designed and trained to predict Cartesian forces as a linear combination of a set of force components in an interatomic basis; these pairwise forces exhibit chemically intuitive profiles and implicitly maintain rotational and translational invariance. Application of the approach to model small molecule systems indicates an accuracy in reconstructed Cartesian atomic forces of ~1 kcal mol−1 Å−1 from the reference force values obtained via density functional theory. The pairF-Net scheme predicts atomic forces at a quantum mechanical level but at a fraction of the cost, enabling molecular dynamics simulations via a chemically intuitive machine learning model.