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

Filippo Bigi, Marcel Langer+1 more|arXiv (Cornell University)|Dec 16, 2024

Machine Learning in Materials ScienceMaterials Science3 citations

TL;DR

This paper investigates non-conservative force models in atomistic machine learning, demonstrating that directly predicting forces without enforcing energy conservation leads to severe instabilities in geometry optimization and molecular dynamics simulations. Despite computational efficiency gains, the lack of energy conservation is difficult to correct, and the authors advocate for combining non-conservative predictions with conservative models to achieve speed and stability.

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, has 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 directly predicting the forces yields a better trade-off between accuracy and computational efficiency, and that energy conservation can be learned during training. This 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. Given the difficulty in monitoring and correcting the lack of energy conservation, direct forces should be used with great care. We show that the best approach to exploit the acceleration they afford is to use them in conjunction with conservative forces. A model can be pre-trained efficiently on direct forces, then fine-tuned using backpropagation. At evaluation time, both force types can be used together to avoid unphysical effects while still benefitting almost entirely from the computational efficiency of direct forces.

Motivation & Objective

• To evaluate the practical viability of non-conservative force models in atomistic simulations, where forces are predicted directly instead of derived from energy.
• To identify fundamental issues arising from energy non-conservation in geometry optimization and molecular dynamics.
• To compare the performance and stability of conservative versus non-conservative models in real simulations.
• To explore whether energy conservation can be effectively learned or corrected in non-conservative models.
• To propose a hybrid strategy using non-conservative forces for acceleration while preserving energy conservation via conservative corrections.

Proposed method

• Train a conservative graph neural network (PET-C) and a non-conservative variant (PET-NC) on the same dataset, with shared message-passing architecture.
• Use the non-conservative model's predictions as fast forces in a multiple time stepping (MTS) integrator, with conservative forces as slow corrections.
• Implement a velocity-Verlet integrator with MTS to simulate NVE and NVT dynamics, using the non-conservative forces for fast steps and conservative forces every M steps.
• Apply a stochastic velocity rescaling (SVR) thermostat to maintain constant temperature in NVT simulations.
• Fine-tune the non-conservative head using the conservative model's output to improve force accuracy while preserving computational speed.
• Compare trajectories from MTS simulations with reference conservative trajectories using structural and kinetic temperature metrics.

Experimental results

Research questions

• RQ1 Can non-conservative force models be reliably used in molecular dynamics simulations without causing instability?
• RQ2 How does energy non-conservation affect the convergence of geometry optimization in machine-learned potentials?
• RQ3 To what extent can energy conservation be learned or corrected in non-conservative models during training?
• RQ4 What is the impact of time-step size and MTS integration order on the stability of non-conservative force simulations?
• RQ5 Can a hybrid approach combining non-conservative and conservative forces achieve both computational efficiency and physical consistency?

Key findings

• Non-conservative force models lead to unstable NVE molecular dynamics trajectories when the multiple time stepping (MTS) factor M exceeds 8, resulting in large kinetic temperature drift.
• Geometry optimization fails to converge reliably with non-conservative forces due to ill-defined energy landscapes and lack of energy conservation.
• MTS simulations with M=8 achieve near-ideal speed-up while maintaining stability and good agreement with reference conservative trajectories.
• Structural correlations (O-O, H-H, orientational) in water simulations using MTS with M=8 show excellent agreement with the reference conservative model, with differences within two standard errors.
• The use of a SVR thermostat enables stable NVT sampling with non-conservative forces, but only when M ≤ 8 to avoid resonance-driven instabilities.
• Fine-tuning the non-conservative head using the conservative model's output improves force accuracy without sacrificing computational efficiency, enabling a practical hybrid approach.