When More Data Hurts: Optimizing Data Coverage While Mitigating Diversity Induced Underfitting in an Ultra-Fast Machine-Learned Potential

TL;DR

This study investigates how training data diversity affects the performance of MLIPs using the Ultra-Fast Force Field to model amorphous silicon nitride and finds that the UF$^3$ variant trained on a subset of the training data, in which nitrogen-rich structures were removed, offered vastly better prediction and simulation accuracy than any other variant.

Abstract

Machine-learned interatomic potentials (MLIPs) are becoming an essential tool in materials modeling. However, optimizing the generation of training data used to parameterize the MLIPs remains a significant challenge. This is because MLIPs can fail when encountering local enviroments too different from those present in the training data. The difficulty of determining \textit{a priori} the environments that will be encountered during molecular dynamics (MD) simulation necessitates diverse, high-quality training data. This study investigates how training data diversity affects the performance of MLIPs using the Ultra-Fast Force Field (UF$^3$) to model amorphous silicon nitride. We employ expert and autonomously generated data to create the training data and fit four force-field variants to subsets of the data. Our findings reveal a critical balance in training data diversity: insufficient diversity hinders generalization, while excessive diversity can exceed the MLIP's learning capacity, reducing simulation accuracy. Specifically, we found that the UF$^3$ variant trained on a subset of the training data, in which nitrogen-rich structures were removed, offered vastly better prediction and simulation accuracy than any other variant. By comparing these UF$^3$ variants, we highlight the nuanced requirements for creating accurate MLIPs, emphasizing the importance of application-specific training data to achieve optimal performance in modeling complex material behaviors.

Figures (4)

• Figure 1: Speed comparison of DFT, GAP, empirical potentials and UF$^3$. The plot shows the speed of DFT, the GAP sin_mlip_1 and UF$^3$ MLIP, and the MG2 mg2, Vashishta vashishta, and Tersoff tersoff empirical potentials. The speed simulations were ran on 4 CPUs for 100 timesteps with a simulation size of 3024 atoms.
• Figure 2: Visualization of the 2-body terms for the UF$^3$ variants. The lines represent the learned two-body interaction for each variant for (a) Si-Si, (b) Si-N, and (c) N-N interactions.
• Figure 3: Validation force predictions for the $\mathrm{UF}^3$ variants The green markers show the predictions for the stoichiometric test set compared to DFT. The red markers show the predictions for the non-stoichiometric test set compared to DFT. The color gradient shows the density of points. The tables show the regression metrics for the variants on both test sets
• Figure 4: Validation simulation results for the $\mathrm{UF}^3$ variants. (a) Shows the performance of elastic properties simulated by the UF$^3$ variants compared to DFT. The solid black circle indicates zero error. The inner and outer circles represent 50% under and over prediction, respectively. The subscript represents the Si$_3$N$_4$ polytype. the number in the spider plots is the mean absolute percent error (MAPE) for all quantities computed compared to DFT. (b,c) Show the structural properties of amorphous Si$_3$N$_4$ at 1700 K for UF$^3$. The initial amorphous structure started from a random configuration of 224 atoms. It was then equilibrated using UF$^3_{\text{final}}$ for 16 ns at 1700 K. This structure was then further equilibrated for an additional 800 ps using either aiMD for the DFT-equilibrated reference or the respective UF$^3$ variant. (b) shows the partial RDF for N-N (bottom), Si-Si (middle), and Si-N (top). The number in the legend is the final density of the amorphous structure. (c) Shows the ADF computed by each variant for N-Si-N (top) and Si-N-Si (bottom) interactions.