Benchmarking Universal Machine Learning Interatomic Potentials for Supported Nanoparticles: Decoupling Energy Accuracy from Structural Exploration

TL;DR

This work addresses the computational bottleneck in modeling supported nanoparticles by benchmarking universal MLIPs (uMLIPs) against a domain-specific DP-UniAlCu baseline for Cu nanoparticles on Al$_2$O$_3$. The study evaluates both global optimization and finite-temperature MD, showing that MACE-OMAT and MatterSim models can match DP-UniAlCu in binding-energy accuracy for small nanoparticles and can discover very stable configurations in some cases, while DP-UniAlCu remains the most reliable and efficient for larger-scale sampling. MD benchmarks indicate uMLIPs reproduce $MSD_{ ext{Cu}}$ and Cu–Al/O RDF trends qualitatively but at roughly two orders of magnitude higher cost, making DP-UniAlCu the preferred choice for long-time simulations. The results suggest uMLIPs are valuable for generating diverse configurations without fine-tuning, but practical workflows may require distillation or targeted fine-tuning to balance accuracy and efficiency.

Abstract

Supported nanoparticle catalysts are widely used in the chemical industry. Computational modeling of supported nanoparticles based on density functional theory (DFT) often involves structural searches of stable local minimum energy configurations and molecular dynamics simulations at finite temperature. These are computationally demanding tasks that are intractable within DFT for large systems. In the last two decades, machine learning interatomic potentials (MLIPs) have been successfully used to substantially increase the size and time scales accessible to simulations that retain DFT accuracy. However, training reliable MLIPs is non-trivial as it requires many costly DFT calculations. Recently, several universal MLIPs (uMLIPs) have been developed, which are trained on large datasets that cover a wide range of molecules and materials. Here, we benchmark the accuracy and the efficiency of these uMLIPs in describing Cu nanoparticles supported on Al$_2$O$_3$ surfaces against our domain-specific DP-UniAlCu model. We find that the MACE-OMAT can reproduce reasonably well the low-energy configurations found in global optimization at an energy accuracy comparable to DP-UniAlCu. Interestingly, the MatterSim-v1.0.0-1M model, which exhibits larger deviations in the binding energies, can find even more stable configurations than the other two models in some supported nanoparticle sizes, showing its capability in structure exploration. For MD simulations, MACE-OMAT and MatterSim-v1.0.0-1M can qualitatively reproduce the mean-squared displacements of Cu atoms (MSD$_\mathrm{Cu}$) predicted by DP-UniAlCu, albeit at roughly two orders of magnitude higher cost. We demonstrate that the uMLIPs can be very useful in simulating supported nanoparticles even without any fine-tuning, though their reduced efficiency remains a limiting factor for large-scale simulations.

Figures (5)

• Figure 1: Several MLIPs are examined for the binding energies of Cu$_{1-21}$ on three Al$_2$O$_3$ surfaces: (a) $\gamma$-Al$_2$O$_3$(100) (b) $\gamma$-Al$_2$O$_3$(110) (c) $\alpha$-Al$_2$O$_3$(0001) (d) violin plots of errors in binding energy. DP-UniAlCu and MACE-UniAlCu have smaller spreads on the binding energy errors since they are specifically trained on these systems. Among uMLIPs, MACE-OMAT and MatterSim-v1.0.0-5M show similar accuracy as DP-UniAlCu, which reproduce the relative binding strength across three surfaces. Degraded performance is observed for MACE-MP and MatterSim-v1.0.0-1M as the former one is trained on a smaller dataset and the latter one is a model with smaller parameters. DPA2-MPTrj shows large energy differences compared to DFT and DPA3-OMAT has reduced errors due to its improved architecture.
• Figure 2: The low-energy configurations of Cu$_{27}$ and Cu$_{38}$ on $\gamma$-Al$_2$O$_3$(100), $\gamma$-Al$_2$O$_3$(110), and $\alpha$-Al$_2$O$_3$(0001) by DFT, DP-UniAlCu (blue), MACE-OMAT (green), and MatterSim-v1.0.0-1M (orange). The DFT configurations are made up of structures obtained from MLIP-based global optimization. Each MLIP provides 50 structures for a given combination of the nanoparticle size and the supporting surface, forming a low-energy ensemble of 150 structures for each system. The arrows indicate the positions of the DFT-minimized global minimum configurations in spectra.
• Figure 3: The low-energy configurations of Cu$_{47}$ and Cu$_{55}$ on $\gamma$-Al$_2$O$_3$(100), $\gamma$-Al$_2$O$_3$(110), and $\alpha$-Al$_2$O$_3$(0001) by DFT, DP-UniAlCu (blue), MACE-OMAT (green), and MatterSim-v1.0.0-1M (orange). The DFT configurations are made up of structures obtained from MLIP-based global optimization. Each MLIP provides 50 structures for a given combination of the nanoparticle size and the supporting surface, forming a low-energy ensemble of 150 structures for each system. The arrows indicate the positions of the DFT-minimized global minimum configurations in spectra.
• Figure 4: For each MLIP, 20 MD simulations starting from the same global minimum configuration of Cu$_{13}$ but initialized from different velocities by Maxwell-Boltzmann distribution at 800 K are performed for 20 ps with a timestep of 2 fs. For AIMD, only one trajectory is performed with the same settings. (a)-(c) The mean square displacement of Cu atoms. The vertical bars are the standard deviations of 20 MD simulations by MLIPs. (d)-(f) The radial distribution functions of Cu-Al. (g)-(i) The radial distribution functions of Cu-O.
• Figure 5: (a)-(c) The mean square displacement of Cu atoms for Cu$_{13}$ on three Al$_2$O$_3$ surfaces at 800 K. (d) The computational performance of DP-UniAlCu, DPA3-OMAT, MACE-OMAT, MACE-UniAlCu, and MatterSim-v1.0.0-1M models on the simulation of an FCC Cu bulk with 2048 atoms. The "katoms*step/s" is defined as the number of thousands of atoms processed per MD step per second. The inset panels show the initial structures of MD simulations.