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在原子模型領域，精確擬合原子間相互作用和計算量之間往往“魚與熊掌不可兼得”：第一性原理計算長于擬合準確性卻因計算量龐大而短于模擬大規模材料體系，經典原子勢計算則恰恰相反。近來，機器學習原子勢（machine learning interatomic potential，MLIP）作為一種新興計算方法，極有潛力解決這一矛盾——在大規模模擬原子體系時保持接近第一性原理計算的準確性。

Fig. 1 Testing of MLIPs.

然而，盡管已有大量研究表明機器學習原子勢能夠精確擬合第一性原理計算（如密度泛函理論）所得的原子體系能量和原子作用力，其能否精確重現原子動力學現象和材料的物理性質這一問題始終懸而未決。

Fig. 2 Diffusions of point defects in Si.

來自美國馬里蘭大學材料科學和工程系的莫一非教授團隊，通過系統性檢測機器學習原子勢和第一性原理計算在分子動力學模擬結果間的差異，識別出數個當下機器學習原子勢的不足之處，提出了新的評價指標，并總結出一套有效的評價指標研究流程。

Fig. 3 Si interstitials by MLIPs.

作者們測試并總結了當前多種機器學習原子勢在硅體系里的表現，觀察到它們在分子動力學模擬中和第一性原理計算的原子運動方式有較大誤差，并進而導致其預測材料物理性質時可能偏離原始值。機器學習原子勢的不足之處集中在：1）原子運動（比如擴散和原子振動），2）缺陷和3）稀有事件這三方面。

Fig. 4 Errors in atom vibrations.

作者發現這些分子動力學模擬上的差異歸咎于機器學習原子勢在能量景觀、形成能和在稀有事件原子上作用力的預測誤差。他們隨后針對稀有事件的原子作用力，提出全新的作用力表現分（force performance score）指標。該指標同時考慮作用力的大小誤差和方向誤差，能有效改進機器學習原子勢的預測準確性。

Fig. 5 Errors of atomic forces.

他們將大量不同機器學習原子勢的表現綜合起來，展現了新評價指標和被預測的物理性質之間的顯著關聯。這一方法有助于評估指標的有效性并建立嚴謹的原子勢檢測流程。

Fig. 6 The performance of RE-enhanced MLIPs.

該研究揭示了傳統的誤差指標在評價機器學習原子勢表現上的不足，為進一步改善機器學習原子勢模型提供了嚴謹的數值依據和指導方向。作者提出的作用力表現分新評價指標流程可廣泛應用于機器學習原子勢的標準檢測。相關論文近期發布于npj?Computational Materials?9:?174?(2023)。手機閱讀原文，請點擊本文底部左下角“閱讀原文”，進入后亦可下載全文PDF文件。

Fig. 7 Process of MLIP training and developing metrics.

Editorial Summary

Citically assessing machine learning interatomic potentials’ performance.

While first-principles computation, such as density functional theory (DFT), provides accurate description of atomic interactions in atomic modeling, its applications are limited to small materials systems of nanometer level and simulations lasting for a few nanoseconds. Alternatively, classical interatomic potentials offer large scale simulations of atomic systems, but they generally lack the accuracy as DFT calculations when describing interatomic bonds. Recently, machine learning interatomic potential (MLIP), as an emerging technique, shows a great opportunity to solve the dilemma between accuracies and computation cost in large-scale atomistic simulations. However, though many studies report that MLIPs have low errors fitting the energies and forces of atomic systems, whether MLIPs can accurately reproduce atomistic dynamics and physical properties of materials remains an open concern.

A research team led by Prof. Yifei Mo from the Department of Materials Science and Engineering at the University of Maryland, USA, systematically investigated state-of-the-art MLIPs. Their comprehensive study revealed discrepancies between ab initio molecular dynamics (AIMD) and MLIP-MD simulations. They identified that these differences primarily manifest in atomic dynamics, including atomic vibrations, defects, and rare events. The discrepancies can be attributed to inaccurate predictions on energy landscapes, formation energies of defects, and forces on atoms involved in rare events. To address these, the team introduced novel evaluation metrics termed ‘force performance scores’ which consider both the force errors in magnitude and direction on rare-event atoms. By testing a number of MLIPs, they established correlations between the metrics and the physical properties predicted. This research not only emphasized the inadequacy of conventional error testing for evaluating MLIP performance but also provided robust insights and guidance to rectify the discrepancies observed in atomic dynamics, defects, and rare events. Their findings have been published in npj Computational Materials 9, 174 (2023).

原文Abstract及其翻譯

Discrepancies and error evaluation metrics for machine learning interatomic potentials (機器學習原子勢的誤差及其評價指標)

Yunsheng Liu,?Xingfeng He?&?Yifei Mo?

Abstract Machine learning interatomic potentials (MLIPs) are a promising technique for atomic modeling. While small errors are widely reported for MLIPs, an open concern is whether MLIPs can accurately reproduce atomistic dynamics and related physical properties in molecular dynamics (MD) simulations. In this study, we examine the state-of-the-art MLIPs and uncover several discrepancies related to atom dynamics, defects, and rare events (REs), compared to ab initio methods. We find that low averaged errors by current MLIP testing are insufficient and develop quantitative metrics that better indicate the accurate prediction of atomic dynamics by MLIPs. The MLIPs optimized by the RE-based evaluation metrics are demonstrated to have improved prediction in multiple properties. The identified errors, the evaluation metrics, and the proposed process of developing such metrics are general to MLIPs, thus providing valuable guidance for future testing and improvements of accurate and reliable MLIPs for atomistic modeling.

摘要

機器學習原子勢（MLIP）這一技術在原子建模領域極具潛力。大量的研究報告稱機器學習原子勢在數值擬合原子能量和力上能達到很小的誤差。然而，機器學習原子勢能否在分子動力學模擬中精確地復現原子層級的動力學現象和相關的物理性質卻是這一技術未解的隱憂。本研究檢驗了當前數個機器學習原子勢并發現它們和第一性原理計算的結果在原子動力學行為、缺陷和稀有事件上有相當的誤差。該研究發現當下廣泛用于測試機器學習原子勢的平均能量誤差和原子力誤差等指標并不能充分地描述它們的表現。研究進而開發了其他量化指標，能更好地展現機器學習原子勢在原子動力學方面的預測準確性。機器學習原子勢在經過這類評價指標的優化后，在多個物理性質的預測上有顯著的提高。本研究中所發現的誤差，開發的評價指標和提出的開發流程可廣泛應用于各類不同機器學習原子勢，對于未來測試、改進、開發精確且可靠的機器學習原子勢具有重要的指導意義。

原創文章，作者：v-suan，如若轉載，請注明來源華算科技，注明出處：http://www.zzhhcy.com/index.php/2023/10/18/e410cc9a0f/

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作用力表現分：消除機器學習原子勢的阿喀琉斯之踵？

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作用力表現分：消除機器學習原子勢的阿喀琉斯之踵？

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