Machine-learned interatomic potentials (MLIPs) are typically trained on datasets that encompass a restricted subset of possible input structures, which presents a potential challenge for their generalization to a broader range of systems outside the training set. Nevertheless, MLIPs have demonstrated impressive accuracy in predicting forces and energies in simulations involving intricate and complex structures. In this paper we aim to take steps towards rigorously explaining the excellent observed generalisation properties of MLIPs. Specifically, we offer a comprehensive theoretical and numerical investigation of the generalization of MLIPs in the context of dislocation simulations. We quantify precisely how the accuracy of such simulations is directly determined by a few key factors: the size of the training structures, the choice of training observations (e.g., energies, forces, virials), and the level of accuracy achieved in the fitting process. Notably, our study reveals the crucial role of fitting virials in ensuring the consistency of MLIPs for dislocation simulations. Our series of careful numerical experiments encompassing screw, edge, and mixed dislocations, supports existing best practices in the MLIPs literature but also provides new insights into the design of data sets and loss functions.

翻译：机器学习原子间势能（MLIPs）通常在包含有限子集输入结构的数据集上进行训练，这对其向训练集外更广泛系统的泛化能力构成潜在挑战。然而，MLIPs在涉及复杂结构的模拟中预测力和能量时展现出令人瞩目的准确性。本文致力于严格解释MLIPs所表现出的卓越泛化特性。具体而言，我们在位错模拟背景下对MLIPs的泛化能力进行了全面理论和数值研究。我们精确量化了此类模拟精度如何直接取决于几个关键因素：训练结构的规模、训练观测值（如能量、力、维里系数）的选择，以及拟合过程中达到的精度水平。值得注意的是，我们的研究揭示了拟合维里系数对确保位错模拟中MLIPs一致性的关键作用。通过涵盖螺型位错、刃型位错和混合位错的一系列精细数值实验，本研究不仅支持了MLIPs文献中的现有最佳实践，还为数据集和损失函数的设计提供了新见解。