Generalizability of Graph Neural Network Force Fields for Predicting Solid-State Properties

TL;DR

The paper addresses the generalizability of graph neural network force fields (GNN-FFs) trained on Lennard-Jones Argon for solid-state properties, extending validation to finite-temperature lattice dynamics and defect processes. It combines Hessian-based phonon analysis, spectral energy density for finite-T phonons and thermal conductivity, and string-method–driven minimum energy paths to benchmark against the reference LJ potential. The results show that the GNN-FF closely reproduces phonon spectra, lifetimes, and thermal conductivity (within ~15%), and captures vacancy diffusion kinetics and energy barriers even when vacancy configurations are not in the training set, supporting the model’s transferability. The study also emphasizes data-coverage strategies and presents a workflow that can guide future MLFF development for complex solid-state materials and defect-driven phenomena.

Abstract

Machine-learned force fields (MLFFs) promise to offer a computationally efficient alternative to ab initio simulations for complex molecular systems. However, ensuring their generalizability beyond training data is crucial for their wide application in studying solid materials. This work investigates the ability of a graph neural network (GNN)-based MLFF, trained on Lennard-Jones Argon, to describe solid-state phenomena not explicitly included during training. We assess the MLFF's performance in predicting phonon density of states (PDOS) for a perfect face-centered cubic (FCC) crystal structure at both zero and finite temperatures. Additionally, we evaluate vacancy migration rates and energy barriers in an imperfect crystal using direct molecular dynamics (MD) simulations and the string method. Notably, vacancy configurations were absent from the training data. Our results demonstrate the MLFF's capability to capture essential solid-state properties with good agreement to reference data, even for unseen configurations. We further discuss data engineering strategies to enhance the generalizability of MLFFs. The proposed set of benchmark tests and workflow for evaluating MLFF performance in describing perfect and imperfect crystals pave the way for reliable application of MLFFs in studying complex solid-state materials.

Figures (7)

• Figure 1: The phonon density of states at $T = 0$ K obtained from Lennard-Jones force field and the GNN-based force field with MAE of 0.02 THz and MaxAE of 0.09 THz.
• Figure 2: The phonon dispersion relation at $T = 0$ K obtained from the reference MD potential and the GNN-based MLFF at (a) $p = 137.1$ bar (training configuration pressure) with MAE of 0.02 THz and MaxAE of 0.07 THz and (b) $p = -2.5$ kbar with MAE of 0.002 THz and MaxAE of 0.06 THz.
• Figure 3: The spectral energy density, $\phi(\bm{k},\omega)$, in eV$\cdot$ps, at $T = 40$ K and $p = 137.1$ bar, obtained from the (a) MD simulation and (b) GNN-MD simulation trajectories.
• Figure 4: The spectral energy density, $\phi(\bm{k},\omega)$, in eV$\cdot$ps, at $T = 40$ K and $p = 137.1$ bar, (a) averaged over the frequency range of $\omega/2\pi = 0.25 \pm 0.02$ THz and (b) calculated at $k_z=\pi/(10a)$.
• Figure 5: (a) The fraction of simulation trajectories in which the vacancy has not jumped as a function of time at $T = 60$ K from the GNN-MD (W.O.V.) simulation. (b) The Arrhenius plot of vacancy jumping rate as a function of $1/T$ . GNN-MD (W.O.V.) and GNN-MD (W.V.) correspond to the MD simulation using the model trained on configurations without and with a single vacancy, respectively.