Gradient-Guided Furthest Point Sampling for Robust Training Set Selection

2025-10-09

AI Summary

In chemical machine learning, large training datasets and poor prediction robustness remain critical challenges; moreover, conventional Furthest Point Sampling (FPS) often under-samples equilibrium molecular geometries in conformational space. To address these issues, we propose Gradient-guided FPS (G-FPS), the first method to incorporate the molecular force norm—i.e., the Euclidean norm of the energy gradient—into the FPS framework. By redefining the distance metric via gradient-based weighting, G-FPS prioritizes high-gradient regions while ensuring adequate coverage of equilibrium structures. On the Styblinski-Tang potential energy surface, G-FPS achieves comparable accuracy using only ~50% of the training samples required by standard FPS. On the MD17 benchmark, models trained with G-FPS exhibit systematically lower prediction errors and variances, outperforming both standard FPS and uniform sampling. Crucially, G-FPS enhances generalization consistency and stability across the full conformational spectrum—from equilibrium to strongly distorted geometries.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Smart training set selections procedures enable the reduction of data needs and improves predictive robustness 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 (Styblinski-Tang function) as well as for molecular dynamics trajectories from the MD17 dataset. Compared to FPS and uniform sampling, our numerical results indicate superior data efficiency and robustness when using GGFPS. 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 two fold reductions in training cost without sacrificing predictive accuracy compared to FPS in the 2-dimensional Styblinksi-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.

Problem

• Improves training set selection for molecular machine learning robustness
• Addresses FPS under-sampling of molecular equilibrium geometries
• Reduces prediction errors and variances in molecular configurations

Innovation

• Gradient Guided Furthest Point Sampling method
• Uses molecular force norms for sampling
• Improves data efficiency and prediction robustness