NEP-CG and NEP-AACG: Efficient coarse-grained and multiscale all-atom-coarse-grained neuroevolution potentials

TL;DR

This work proposes a method to generate low-noise training data based on the potential of mean force by constraining CG beads during atomistic simulations and accumulating time-averaged forces, and provides a robust framework for constructing accurate, transferable, and efficient CG models across diverse systems.

Abstract

Machine-learned coarse-grained (CG) models often suffer from noisy training data, limiting their accuracy and transferability. We propose a method to generate low-noise training data based on the potential of mean force by constraining CG beads during atomistic simulations and accumulating time-averaged forces. Implemented within the neuroevolution potential (NEP) framework, our approach achieves training accuracy comparable to atomistic models trained on density functional theory data. For liquid water, the NEP-CG model accurately reproduces densities from 1 bar to 1 GPa, successfully extrapolating beyond the 0.5 GPa training limit, with a virial correction essential for the correct equation of state. For an anisotropic C$_{60}$ monolayer, distinguishing crystallographically distinct bead types reduces stress errors by an order of magnitude and captures directional thermal conductivity. We further introduce a multiscale NEP-AACG model integrating all-atom (AA) and CG degrees of freedom, demonstrated for gold nanowire fracture at an experimentally relevant strain rate. Computational speeds for NEP-CG models reach hundreds to thousands of ns/day using a single consumer-grade GPU. This work provides a robust framework for constructing accurate, transferable, and efficient CG models across diverse systems.

Figures (8)

• Figure 1: Parity plots comparing forces and stresses predicted by NEP-CG models against NEP-AA reference data for liquid water at 300 K. (a,b) Results from a NEP-CG model trained against instantaneous forces and stresses sampled at 1 bar, showing systematic deviation from the $y=x$ line and significant scatter. (c,d) Results from a NEP-CG model trained against ensemble-averaged forces and stresses using our constrained dynamics approach, incorporating data sampled across target pressures from 1 bar to 0.5 GPa. The ensemble-based model demonstrates excellent agreement and substantially reduced errors across the entire pressure range. Different colors correspond to different force and virial components.
• Figure 2: Structural properties and equation of state of liquid water predicted by the NEP-CG model compared to NEP-AA reference data at 300 K. (a) Radial distribution functions $g(r)$ for CG beads at 1 bar and 0.5 GPa, showing excellent structural agreement. (b) Density as a function of pressure from 1 bar to 1 GPa. Results are shown for the NEP-AA reference, the NEP-CG model with virial correction (Eq. \ref{['equation:virial_correction']}), and the NEP-CG model without virial correction. The virial-corrected model accurately reproduces NEP-AA densities across the entire pressure range.
• Figure 3: Parity plots comparing forces and stresses predicted by NEP-CG models against NEP-AA reference data for the QHP-C$_{60}$ monolayer at 300 K under various in-plane strain states. (a,b) Results from a one-type NEP-CG model treating all C$_{60}$ molecules as identical beads, exhibiting systematic errors. (c,d) Results from a two-type NEP-CG model distinguishing the two crystallographically distinct C$_{60}$ molecules, accounting for directional dependence of covalent linkages. The two-type model demonstrates substantially improved agreement, particularly for stress components.
• Figure 4: Lattice thermal conductivity of the QHP-C$_{60}$ monolayer as a function of production time in HNEMD simulations. (a) Thermal conductivity along the $x$-direction (average of $[110]$ and $[1\bar{1}0]$ directions). (b) Thermal conductivity along the $y$-direction ($[010]$ direction). Lighter lines show five independent simulations, darker lines their average, and shaded areas the standard error bounds. CG results are scaled by a factor of 60 to account for reduced degrees of freedom.
• Figure 5: Parity plots for (a) forces and (b) stresses predicted by the unified NEP-AACG model compared to reference data. Squares represent the pure AA dataset (DFT references song2024nc). Circles represent both pure CG and mixed AACG datasets (references from constrained NEP-AA simulations). All predictions are from the same NEP-AACG model, demonstrating its ability to simultaneously describe atomistic, coarse-grained, and mixed-resolution configurations.