Scalable Training of Neural Network Potentials for Complex Interfaces Through Data Augmentation

TL;DR

The paper addresses the high data and computational demands of training neural network potentials for complex material interfaces. It introduces a GPR-based data-augmentation strategy (GPR-ANN) that indirectly incorporates force information by generating synthetic energies from local GPR surrogates, enabling efficient energy-only training with uncertainty estimates for active learning. Across H2, EC dimers, and EC on Li metal surfaces, GPR-ANN achieves accuracy and robustness comparable to direct force training but with substantially reduced memory and compute requirements, thanks to local GPR models and scalable augmentation factors. This approach yields a practical, scalable pathway to high-fidelity interfacial potentials, facilitating large-scale simulations relevant to battery interfaces and other heterogeneous condensed-phase systems.

Abstract

Artificial neural network (ANN) potentials enable highly accurate atomistic simulations of complex materials at unprecedented scales. Despite their promise, training ANN potentials to represent intricate potential energy surfaces (PES) with transferability to diverse chemical environments remains computationally intensive, especially when atomic force data are incorporated to improve PES gradients. Here, we present an efficient ANN potential training methodology that uses Gaussian process regression (GPR) to incorporate atomic forces into ANN training, leading to accurate PES models with fewer additional first-principles calculations and a reduced computational effort for training. Our GPR-ANN approach generates synthetic energy data from force information in the reference dataset, thus augmenting the training datasets and bypassing direct force training. Benchmark tests on hybrid density-functional theory data for ethylene carbonate (EC) molecules and Li metal-EC interfaces, relevant for lithium metal battery applications, demonstrate that GPR-ANN potentials achieve accuracies comparable to fully force-trained ANNs with a significantly reduced computational overhead. Detailed comparisons show that the method improves both data efficiency and scalability for complex interfaces and heterogeneous environments. This work establishes the GPR-ANN method as a powerful and scalable framework for constructing high-fidelity machine learning interatomic potentials, offering the computational and memory efficiency critical for the large-scale simulations needed for the simulation of materials interfaces.

Figures (26)

• Figure 1: Indirect force training with the GPR-ANN approach. (Step 1) The reference data (black circles) consists of atomic structures ($\sigma$), their energies ($E(\sigma)$) and corresponding atomic forces ($F_{j}(\sigma)$) from electronic structure calculations for structures sampling target potential energy surfaces (PES, thick gray lines). Each subset contains related structures with the same number of atoms. (Step 2) For each subset, Gaussian process regression (GPR) models can efficiently interpolate the potential energy surface based on the energies and atomic forces (red lines). The GPR models can then be used to generate synthetic data by labeling additional related structures (empty circles) with energies. Structures for which the GPR model reports a high uncertainty are evaluated with the reference electronic structure method. (Step 3) Finally, the original structures and their energies can be combined with the additional structures and their GPR energies (red triangles) into a unified overall data set that can be used for efficient energy-only training of general ANN potentials (yellow lines).
• Figure 2: Comparison of the different ANN potential training strategies for an H2 molecule. The same seven reference data points (black circles) sampled from the target potential energy surface of a H2 dimer (dashed black line) were used to assess the accuracy and robustness of ANN potentials obtained by training with the four strategies detailed in the main text: a, energy-only training, indirect force training with b, the Taylor-expansion method and, c, the GPR-ANN method, and d, direct force training. The insets show zoomed-in views of the regions marked with rectangles. The mean predicted energies (top) and forces (bottom) of 10 ANN potentials are shown as solid lines, and the shaded regions indicate the 99% confidence interval (CI) as a measure of uncertainty. For the data-augmentation approaches, Taylor-ANN and GPR-ANN, the seven reference energies were supplemented with 14 predicted energies (green squares in b and red triangles in c), and the corresponding H2 structures were generated with atomic displacements of $\delta=\pm{}0.008$ Å and $\delta=\pm{}0.055$ Å, respectively. The Taylor-ANN and GPR-ANN potentials corresponding to the optimal atomic displacements are shown, and results from other $\delta$ variables can be found in Figures S4--7. The accuracy and robustness of the training strategies are quantified by the e, mean absolute error (MAE) and, f, mean standard deviation (MSD) of the energy and the g, MAE and g, MSD of the force, respectively. For the data-augmentation methods, these measures depend on the displacement length and are shown as a function of $\delta$.
• Figure 3: Comparison of the accuracy and robustness of the four ANN training methods for ethylene carbonate dimer structures. The mean absolute error (MAE) and mean standard deviation (MSD) over a committee of 10 ANN potentials are shown for a the energy, b the absolute magnitude of the forces, and c the force direction. These metrics are shown for ANN potentials obtained from energy-only training (dashed purple line), indirect force training with the Taylor-ANN (green squares), and the GPR-ANN (orange triangles) approach, and direct force training with 10% forces (dashed light blue line) and 100% force information (dashed dark blue line).
• Figure 4: Detailed analysis of the atomic forces in ethylene carbonate dimers predicted with the different training approaches.a-d, Correlation of the magnitude of the forces predicted by ANN potentials with the DFT reference. e-h, Error in force direction with respect to DFT reference. The predictions were made by a committee of 10 potentials obtained from energy-only training (a, e), implicit force training with the Taylor-ANN (b, f) and GPR-ANN (c, g) methods, and direct force training (d, h). The color indicates the frequency of occurrence using a logarithmic scale. The solid black line in the top panels a-d corresponds to perfect correlation with the DFT reference, and the dashed black lines indicate differences greater than 1 eV/Å. Optimal parameters were used for all force training methods: Taylor-ANN ($\delta$=0.003 Å, multiple=64), GPR-ANN ($\delta$=0.021 Å, multiple=64), and direct force training (100% forces, alpha=0.3).
• Figure 5: Comparison of the accuracy and robustness of the four ANN training methods for an ethylene carbonate molecule adsorbed on the lithium metal (100) surface. The mean absolute error (MAE) and mean standard deviation (MSD) based on a committee of 10 ANN potentials are shown for the a, energy, b, absolute force magnitude, and c force direction. Results are shown for energy-only training (dashed purple lines), indirect force training with the Taylor-ANN (green squares) and GPR-ANN (orange triangles) data-augmentation methods, and direct force training with 10% (dashed light blue lines) and 100% (dashed dark blue lines) force information.