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在原子模型領(lǐng)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(zhǔn)確性卻因計算量龐大而短于模擬大規(guī)模材料體系，經(jīng)典原子勢計算則恰恰相反。近來，機(jī)器學(xué)習(xí)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(guī)模模擬原子體系時保持接近第一性原理計算的準(zhǔn)確性。

作用力表現(xiàn)分：消除機(jī)器學(xué)習(xí)原子勢的阿喀琉斯之踵？

Fig. 1 Testing of MLIPs.

然而，盡管已有大量研究表明機(jī)器學(xué)習(xí)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(xiàn)原子動力學(xué)現(xiàn)象和材料的物理性質(zhì)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(xué)材料科學(xué)和工程系的莫一非教授團(tuán)隊，通過系統(tǒng)性檢測機(jī)器學(xué)習(xí)原子勢和第一性原理計算在分子動力學(xué)模擬結(jié)果間的差異，識別出數(shù)個當(dāng)下機(jī)器學(xué)習(xí)原子勢的不足之處，提出了新的評價指標(biāo)，并總結(jié)出一套有效的評價指標(biāo)研究流程。

Fig. 3 Si interstitials by MLIPs.

作者們測試并總結(jié)了當(dāng)前多種機(jī)器學(xué)習(xí)原子勢在硅體系里的表現(xiàn)，觀察到它們在分子動力學(xué)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(jìn)而導(dǎo)致其預(yù)測材料物理性質(zhì)時可能偏離原始值。機(jī)器學(xué)習(xí)原子勢的不足之處集中在：1）原子運動（比如擴(kuò)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(fā)現(xiàn)這些分子動力學(xué)模擬上的差異歸咎于機(jī)器學(xué)習(xí)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(yù)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(xiàn)分（force performance score）指標(biāo)。該指標(biāo)同時考慮作用力的大小誤差和方向誤差，能有效改進(jìn)機(jī)器學(xué)習(xí)原子勢的預(yù)測準(zhǔn)確性。

Fig. 5 Errors of atomic forces.

他們將大量不同機(jī)器學(xué)習(xí)原子勢的表現(xiàn)綜合起來，展現(xiàn)了新評價指標(biāo)和被預(yù)測的物理性質(zhì)之間的顯著關(guān)聯(lián)。這一方法有助于評估指標(biāo)的有效性并建立嚴(yán)謹(jǐn)?shù)脑觿輽z測流程。

Fig. 6 The performance of RE-enhanced MLIPs.

該研究揭示了傳統(tǒng)的誤差指標(biāo)在評價機(jī)器學(xué)習(xí)原子勢表現(xiàn)上的不足，為進(jìn)一步改善機(jī)器學(xué)習(xí)原子勢模型提供了嚴(yán)謹(jǐn)?shù)臄?shù)值依據(jù)和指導(dǎo)方向。作者提出的作用力表現(xiàn)分新評價指標(biāo)流程可廣泛應(yīng)用于機(jī)器學(xué)習(xí)原子勢的標(biāo)準(zhǔn)檢測。相關(guān)論文近期發(fā)布于npj?Computational Materials?9:?174?(2023)。手機(jī)閱讀原文，請點擊本文底部左下角“閱讀原文”，進(jìn)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(jī)器學(xué)習(xí)原子勢的誤差及其評價指標(biāo))

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(jī)器學(xué)習(xí)原子勢（MLIP）這一技術(shù)在原子建模領(lǐng)域極具潛力。大量的研究報告稱機(jī)器學(xué)習(xí)原子勢在數(shù)值擬合原子能量和力上能達(dá)到很小的誤差。然而，機(jī)器學(xué)習(xí)原子勢能否在分子動力學(xué)模擬中精確地復(fù)現(xiàn)原子層級的動力學(xué)現(xiàn)象和相關(guān)的物理性質(zhì)卻是這一技術(shù)未解的隱憂。本研究檢驗了當(dāng)前數(shù)個機(jī)器學(xué)習(xí)原子勢并發(fā)現(xiàn)它們和第一性原理計算的結(jié)果在原子動力學(xué)行為、缺陷和稀有事件上有相當(dāng)?shù)恼`差。該研究發(fā)現(xiàn)當(dāng)下廣泛用于測試機(jī)器學(xué)習(xí)原子勢的平均能量誤差和原子力誤差等指標(biāo)并不能充分地描述它們的表現(xiàn)。研究進(jìn)而開發(fā)了其他量化指標(biāo)，能更好地展現(xiàn)機(jī)器學(xué)習(xí)原子勢在原子動力學(xué)方面的預(yù)測準(zhǔn)確性。機(jī)器學(xué)習(xí)原子勢在經(jīng)過這類評價指標(biāo)的優(yōu)化后，在多個物理性質(zhì)的預(yù)測上有顯著的提高。本研究中所發(fā)現(xiàn)的誤差，開發(fā)的評價指標(biāo)和提出的開發(fā)流程可廣泛應(yīng)用于各類不同機(jī)器學(xué)習(xí)原子勢，對于未來測試、改進(jìn)、開發(fā)精確且可靠的機(jī)器學(xué)習(xí)原子勢具有重要的指導(dǎo)意義。

原創(chuàng)文章，作者：v-suan，如若轉(zhuǎn)載，請注明來源華算科技，注明出處：http://m.xiubac.cn/index.php/2023/10/18/e410cc9a0f/

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作用力表現(xiàn)分：消除機(jī)器學(xué)習(xí)原子勢的阿喀琉斯之踵？

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作用力表現(xiàn)分：消除機(jī)器學(xué)習(xí)原子勢的阿喀琉斯之踵？