Aluminum solidification and nanopolycrystal deformation via a Graph Neural Network Potential and Million-Atom Simulations

Abstract

Solidification governs the microstructure and, therefore, the mechanical response of metal components, yet the atomistic details of nucleation and defect formation are often difficult to determine experimentally. Molecular dynamics can bridge this gap, but only if the interatomic model is both accurate and computationally efficient. Here, we develop a Machine Learning Potential (MLP) for aluminum and demonstrate its near ab initio fidelity when trained with the sequential-refinement workflow that fine-tunes the model on low-energy structures. The favorable scaling of the model enables nanosecond simulations involving millions of atoms, thereby overcoming finite-size effects in simulations of polycrystalline solidification and subsequent mechanical testing. Comparison with classical potentials and recent MLP models, including a general-purpose model, shows that inaccuracies in stacking-fault energetics and diffusion can lead to qualitatively incorrect solidified grain structures and post-solidification mechanical behavior. Since our framework is based on an equivariant graph neural network, it allows for straightforward extensions to multi-component systems, providing valuable guidance for the future design and fine-tuning of both specialized and universal MLPs in computational mechanics simulations.

Figures (11)

• Figure 1: Sequential refinement workflow in three stages. First, the GNNP is pre-trained on the ANI-Al dataset, generated via an active learning loop during training of the corresponding ANI-Al potential. We refer to the resulting model as GNNP-Al (non-refined). Using the ANI-Al model, we generate additional low-energy (LE) samples to refine the pre-trained model in the second stage. In the last step, the refined model is trained on a weighted combination of both datasets, called ANI-Al+, to yield the final GNNP-Al model. The components in the dashed box are part of the work by Smith et al. smith2021automated
• Figure 2: Energies $U$ (a) and force components $F$ (b) predicted by the tested potentials compared to the reference label. The data points correspond to a random subset of the test set of the ANI-Al dataset smith2021automated. We excluded predictions from the ANI-Al smith2021automated and UMA wood2025family models as they are indistinguishable from GNNP-Al. Energies are shifted so that the lowest-energy state is set to zero, enabling comparability across models. Some outliers predicted by the Mendelev et al. mendelev2008analysis model fall outside of the plot range.
• Figure 3: Average inference time $\langle t \rangle$ across 100 runs (a) and peak memory usage $M_{max}$ (b) of the tested MLPs for increasing system sizes, with the number of atoms $N_a$ reaching up to 64000. Error bars represent one standard deviation. The star indicates the largest system size before an out-of-memory error occurred. We performed all tests on a single NVIDIA A100 80GB GPU.
• Figure 4: (a) Energies $U$ of the three competing lowest energy crystal structures, face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC), with varying per-atom volume $V$. Squares, hexagons, and diamonds denote FCC, HCP, and BCC, respectively. (b) Stacking fault energy $\gamma$ plotted against the normalized displacement $d$ along the fault vector in $\left< 112 \right>$ direction. The dashed gray line at 1/3 corresponds to a stacking fault where FCC locally resembles HCP. The reference density functional theory (DFT) data in both sub-figures were taken from Smith et al. smith2021automated. Predictions by classical potentials are excluded for readability.
• Figure 5: Elasticity tensor components $C_{11}$ (a), $C_{12}$ (b), and $C_{44}$ (c) and lattice parameter $a$ (d) of an FCC crystal as a function of temperature $T$ across the solid range. Experimental values are taken from Kamm and Alers kamm1964low and Gerlich and Fischer gerlich1969high for the low and high temperature elasticity components, respectively. For the lattice parameter, experimental values correspond to work by Touloukian et al. touloukian1975thermal.