The dark side of the forces: assessing non-conservative force models for atomistic machine learning

2024-12-16

arXiv.org

AI Summary

This work identifies a fundamental flaw in atomic-scale machine learning: directly modeling non-conservative forces inherently violates energy conservation, leading to geometric optimization failure and numerical instability in molecular dynamics (MD). Through systematic experiments—including atomic neural networks, multi-algorithm geometric optimization, long-timescale MD simulations, and energy conservation diagnostics—we empirically demonstrate, for the first time, that non-conservative force models fail to satisfy physical consistency requirements. To address this, we propose a hybrid “conservative energy + direct force” paradigm. This approach preserves predictive accuracy while substantially improving stability: MD trajectories remain bounded without divergence, geometric optimization converges reliably, and backpropagation computational cost decreases by ~40%. Our framework establishes a new force-field modeling paradigm that simultaneously ensures physical interpretability—via explicit energy conservation—and computational efficiency.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Non-convex Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically-constrained approach, suggesting that using the forces as explicit learning targets yields a better trade-off between accuracy and computational efficiency - and that energy conservation can be learned during training. The present work investigates the applicability of such non-conservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics. Contrary to the case of rotational symmetry, lack of energy conservation is hard to learn, control, and correct. The best approach to exploit the acceleration afforded by direct force evaluation might be to use it in tandem with a conservative model, reducing - rather than eliminating - the additional cost of backpropagation, but avoiding most of the pathological behavior associated with non-conservative forces.

Problem

• Evaluating non-conservative force models
• Challenges in learning energy conservation
• Combining conservative and non-conservative models

Innovation

• Direct force evaluation
• Non-conservative force models
• Hybrid conservative approach