npj Computational Materials

Performance of two complementary machine-learned potentials in modelling chemically complex systems

Konstantin Gubaev, Viktor Zaverkin, Prashanth Srinivasan, Andrew Ian Duff, Johannes K？stner & Blazej Grabowski

npj Computational Materials 9: 129 (2023)

doi.org/10.1038/s41524-023-01073-w

Published online: 25 July 2023
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Abstract: Chemically complex multicomponent alloys possess exceptional properties derived from an inexhaustible compositional space. The complexity however makes interatomic potential development challenging. We explore two complementary machine-learned potentials—the moment tensor potential (MTP) and the Gaussian moment neural network (GM-NN)—in simultaneously describing configurational and vibrational degrees of freedom in the Ta-V-Cr-W alloy family. Both models are equally accurate with excellent performance evaluated against density-functional-theory. They achieve root-mean-square-errors (RMSEs) in energies of less than a few meV/atom across 0 K ordered and high-temperature disordered configurations included in the training. Even for compositions not in training, relative energy RMSEs at high temperatures are within a few meV/atom. High-temperature molecular dynamics forces have similarly small RMSEs of about 0.15 eV/？ for the disordered quaternary included in, and ternaries not part of training. MTPs achieve faster convergence with training size; GM-NNs are faster in execution. Active learning is partially beneficial and should be complemented with conventional human-based training set generation.

摘要: 化学复杂的多元合金具有源自无穷无尽的组成空间的卓越性质。然而，其复杂性使得原子间势的开发具有挑战性。我们探索了两个互补的机器学习势函数—矩张量势（MTP）和高斯矩神经网络（GM-NN）— 同时描述Ta-V-Cr-W合金家族的构型和振动自由度。密度泛函理论评估这两种模型同样准确，性能优异。它们在训练中包括的0 K有序和高温无序构型上的能量均方根误差（RMSEs）小于几个meV/原子。即使对于不在训练中的组分，高温下的相对能量RMSEs也在几个meV/原子。对于包括在训练中的无序四元系和不在训练中的三元系，高温分子动力学力的RMSE也非常小，约为0.15 eV/？。MTP随着训练规模变大实现更快的收敛；GM-NN执行速度更快。主动学习在一定程度上是有益的，应该与传统的基于人工生成的训练集相辅相成。

Editorial Summary

The Secret Weapon of Chemically Complex Systems: Machine-Learned Potentials

Multi-component alloys, particularly high-entropy alloys (HEAs), have garnered widespread interest in the field of materials science due to their exceptional properties such as high tensile and yield strength, as well as high ductility. However, the development of accurate and robust interatomic potential functions poses a challenge, mainly attributed to their complex chemical compositions. In this context, this study explores the performance of two complementary machine learning potential functions in modeling chemically complex systems. A team led by Prof. Konstantin Gubaev and Prof. Viktor Zaverkin from the Institute of Materials Science at the University of Stuttgart, Germany, have developed and compared two machine learning potential functions, namely the Matrix Tensor Potential (MTP) and Gaussian Matrix Neural Network (GM-NN). These models were employed to model the configurational and vibrational degrees of freedom in the Ta-V-Cr-W high-entropy alloy family and evaluate their performance in simulating complex multi-component chemical systems. The research findings are as follows: 1. Both MTP and GM-NN models exhibit comparable accuracy in describing the performance of the Ta-V-Cr-W high-entropy alloy. 2. Accurately predict the 0 K energy and forces of subsystems within the training dataset, with energy Root Mean Square Errors (RMSEs) measuring only a few meV/atom. 3. Accurately predict the forces at elevated temperatures for both in-distribution disordered quaternary subsystems and out-of-distribution ternary subsystems, with RMSEs the range of 0.18 eV/？. 4. Reasonably predict relative energies relevant to thermodynamic properties, with RMSEs of 5.5 meV/atom. 5. Active learning strategies, in conjunction with human inspection, complement each other in enhancing the performance of the models. This research provides valuable insights into addressing the modeling and analysis challenges of chemically complex multi-component systems.

化学复杂体系的秘密武器：机器学习势函数

多元合金，特别是高熵合金（HEAs），因其高拉伸和屈服强度、高延展性等优越性能在材料科学领域引起了广泛的兴趣。然而，由于其复杂的化学成分，开发准确且稳健的原子间势函数具有挑战。在此背景下，本研究探讨了两种互补的机器学习势函数在建模化学复杂系统的性能。来自德国斯图加特大学材料科学研究所和理论化学研究所Konstantin Gubaev和Viktor Zaverkin研究团队，开发并比较了两种机器学习势函数，即矩张量势函数（MTP）和高斯矩神经网络（GM-NN），用于建模Ta-V-Cr-W高熵合金家族的构型和振动自由度，并评估了它们在模拟化学复杂多成分系统方面的性能。研究结果表明：1. MTP和GM-NN模型在描述Ta-V-Cr-W高熵合金性能方面表现出相同的准确性。2. 能够准确预测包含在训练数据中的分布内子系统的0 K能量和力，能量均方根误差（RMSEs）小于几个meV/原子。3. 能够准确预测分布内无序四元子系统和分布外三元子系统的高温构型下的力，均方根误差在0.18 eV/？范围内。4. 能够较准确预测与热力学性质相关的相对能量，RMSEs为5.5 meV/原子。5. 主动学习和人工检查相辅相成，提高了模型性能。该研究为解决化学复杂多成分系统的建模和分析问题提供了有价值的见解。