Gradient-Guided Furthest Point Sampling for Robust Training Set Selection

Abstract

Training set sampling methods are used to improve model performance and lower data costs in machine learning problems relevant to chemistry. We introduce Gradient Guided Furthest Point Sampling (GGFPS), a simple extension of Furthest Point Sampling (FPS) that leverages molecular force norms to guide efficient sampling of configurational spaces of molecules. Numerical evidence is presented for a toy system (the Styblinski-Tang function) as well as for molecular dynamics trajectories from the MD17 dataset. Our numerical results indicate superior data efficiency and model robustness when using GGFPS compared to FPS and uniform random sampling (URS), as well as established supervised FPS-style selectors, PCov-FPS and PCov-CUR. Distribution analysis of the MD17 data suggests that FPS systematically under-samples equilibrium geometries, resulting in large test errors for relaxed structures. GGFPS cures this artifact and (i) enables up to twofold reductions in training cost without sacrificing predictive accuracy compared to FPS in the 2-dimensional Styblinski-Tang system, (ii) systematically lowers prediction errors for equilibrium as well as strained structures in MD17, and (iii) systematically decreases prediction error variances across all of the MD17 configuration spaces. These results suggest that gradient-aware sampling methods hold great promise as effective training set selection tools, and that naive use of FPS may result in imbalanced training and inconsistent prediction outcomes.