论文标题

QM/MM晶体缺陷模型的后验误差估计和适应性

A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects

论文作者

Wang, Yangshuai, Kermode, James R., Ortner, Christoph, Zhang, Lei

论文摘要

杂交量子/分子力学(QM/mm)模型在分子模拟中起关键作用。这些模型在准确性,超过纯MM模型和计算效率之间提供了平衡,这比纯QM模型具有优势。已经开发了自适应方法来进一步改善这种平衡,通过必要时可以在线选择QM和MM子系统。我们提出了一种新颖且可靠的自适应QM/mm方法,用于实践材料缺陷模拟。为了确保与QM参考模型的数学一致性,我们将机器学习的原子质势(MLIP)作为MM模型。我们的自适应QM/MM方法利用了一个基于残差的误差估计器,该误差估计器为近似误差提供了上限和下限,从而表明其可靠性和效率。此外,我们引入了一种能够对QM/MM分区更新的新型自适应算法。此更新基于提出的基于残差的误差估计器,涉及求解免费接口运动问题,该问题是使用快速行进方法有效实现的。我们通过在各种晶体缺陷上的数值测试来证明方法的鲁棒性。

Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM models. Adaptive approaches have been developed to further improve this balance by allowing on-the-fly selection of the QM and MM subsystems as necessary. We propose a novel and robust adaptive QM/MM method for practical material defect simulations. To ensure mathematical consistency with the QM reference model, we employ machine-learning interatomic potentials (MLIPs) as the MM models. Our adaptive QM/MM method utilizes a residual-based error estimator that provides both upper and lower bounds for the approximation error, thus indicating its reliability and efficiency. Furthermore, we introduce a novel adaptive algorithm capable of anisotropically updating the QM/MM partitions. This update is based on the proposed residual-based error estimator and involves solving a free interface motion problem, which is efficiently achieved using the fast marching method. We demonstrate the robustness of our approach via numerical tests on a wide range of crystalline defects.

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