深度原子間勢函數(shù)是基于機器學(xué)習(xí)的方法構(gòu)建的高精度原子間相互作用勢能函數(shù)，可提高分子動力學(xué)模擬的效率。對于復(fù)雜的多元固態(tài)鋰電池材料，訓(xùn)練集的構(gòu)建對于高精度的原子間相互作用勢能函數(shù)的開發(fā)尤為重要。因此，設(shè)計一種高效的策略，以生成全面的訓(xùn)練集來準(zhǔn)確模擬這些材料中的不同原子環(huán)境和復(fù)雜界面現(xiàn)象，是確保模擬結(jié)果可靠的關(guān)鍵步驟。

廈門大學(xué)物理學(xué)系吳順情教授團隊提出基于主成分分析（Principal Component Analysis，PCA）的訓(xùn)練集收斂策略。該策略通過計算訓(xùn)練集和測試集的覆蓋范圍，確保了迭代訓(xùn)練的準(zhǔn)確性。經(jīng)過訓(xùn)練開發(fā)的固態(tài)電解質(zhì)鋰鑭鋯氧（Li₇La₃Zr₂O₁₂，LLZO）原子間相互作用勢函數(shù)模型能精確描述結(jié)構(gòu)和動力學(xué)性質(zhì)，并成功預(yù)測了LLZO的相變行為，且計算成本遠低于密度泛函理論計算。

Fig. 2: Error verification of the iterative process.

通過基礎(chǔ)訓(xùn)練集獲得初始勢函數(shù)，用于模擬非晶材料測試誤差并迭代優(yōu)化，研究團隊獲得了精確全面的勢函數(shù)模型。通過PCA計算測試集在訓(xùn)練集中的覆蓋率，確保誤差收斂。結(jié)果表明，覆蓋率與誤差率高度相關(guān)，證明了覆蓋率能夠反映訓(xùn)練集的完備性。

該原子間勢與從頭算分子動力學(xué)（AIMD）計算所得的徑向分布函數(shù)（Radial Distribution Function，RDF）高度吻合，驗證了該勢函數(shù)對LLZO系統(tǒng)動力學(xué)性質(zhì)的精確描述。此外，模擬的LLZO的四方–立方相轉(zhuǎn)變溫度和固液相熔化溫度以及熱膨脹系數(shù)與實驗相符。結(jié)構(gòu)準(zhǔn)確性通過XRD圖譜和RDF得到證實。

該研究團隊開發(fā)的高效、精確的機器學(xué)習(xí)勢函數(shù)的構(gòu)建方法，為研究固態(tài)鋰電池中的微尺度界面現(xiàn)象提供了有利工具，也為深入理解和優(yōu)化基于LLZO的固態(tài)電池的復(fù)雜過程提供原子級見解。相關(guān)論文近期發(fā)布于npj?Computational Materials?10:?57?(2024). 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. 5: Coverage analysis and XRD comparison of the phase change process.

Editorial Summary

Deep Interatomic Potential (DP) is a high-precision interatomic interaction potential function constructed based on machine learning methods, which can improve the efficiency of molecular dynamics simulations. For complex multi-component solid-state lithium battery materials, the construction of training sets is particularly important for the development of high-precision inter-atomic interaction potential functions. Therefore, designing an efficient method to generate comprehensive training sets to accurately simulate the various atomic environments and complex interfacial phenomena in these materials is a critical step to ensure reliable simulation results.

A research team led by Professor Wu Shunqing from the Department of Physics at Xiamen University, China, proposed utilizing principal component analysis (PCA) to calculate the coverage range of the training and test sets as the convergence criterion for iterative training. The Li₇La₃Zr₂O₁₂(LLZO) interatomic interaction potential model obtained after training not only accurately describes the structural and dynamic properties but also predicts phase transition behavior, with a computational cost much lower than density functional theory.

Obtained initial potential from the basic training set, simulated amorphous materials for error testing, and iterated to converge errors, resulting in an accurate and comprehensive potential function. By computing the coverage rate of the test set in the training set using PCA, they evaluated whether the error converged during the iterative process. Their results demonstrated a high correlation between the coverage rate and the error rate, proving that the coverage rate can reflect the completeness of the training set.

The interatomic potential showed excellent agreement with the radial distribution function (RDF) obtained from ab initio molecular dynamics (AIMD) calculations, indicating that the potential function can accurately describe the dynamic properties of the LLZO system. In simulating the phase transition process of LLZO, the tetragonal-cubic phase transition temperature and solid-liquid melting temperature were observed, and the calculated thermal expansion coefficient was consistent with experimental values. The structural accuracy was verified by comparing XRD patterns and RDFs, while the reliability of the results was demonstrated by calculating the coverage rate of structural features in the solid and liquid phases.

The research team developed a generalizable method for training high-precision machine learning potentials. Moreover, the DP model provides an accurate and efficient tool for investigating microscale interfacial phenomena in solid-state lithium batteries, which is challenging in experiments. The accuracy, transferability, and convergence of the interatomic potential make it a valuable tool for conducting extensive simulations, providing atomic-level insights into the complex processes involved in optimizing the performance of LLZO-based solid-state batteries. Thisarticle was recently?published in?npj?Computational Materials?10:?57?(2024).

原文Abstract及其翻譯

Principal component analysis enables the design of deep learning potential precisely capturing LLZO phase transitions (主成分分析助力深度學(xué)習(xí)勢精確捕獲 LLZO 相變)

Yiwei You, Dexin Zhang, Fulun Wu, Xinrui Cao, Yang Sun, Zi-Zhong Zhu & Shunqing Wu?

Abstract The development of accurate and efficient interatomic potentials using machine learning has emerged as an important approach in materials simulations and discovery. However, the systematic construction of diverse, converged training sets remains challenging. We develop a deep learning-based interatomic potential for the Li₇La₃Zr₂O₁₂(LLZO) system. Our interatomic potential is trained using a diverse dataset obtained from databases and first-principles simulations. We propose using the coverage of the training and test sets as the convergence criteria for the training iterations, where the coverage is calculated by principal component analysis. This results in an accurate LLZO interatomic potential that can describe the structure and dynamical properties of LLZO systems meanwhile greatly reducing computational costs compared to density functional theory calculations. The interatomic potential accurately describes radial distribution functions and thermal expansion coefficient consistent with experiments. It also predicts the tetragonal-to-cubic phase transition behaviors of LLZO systems. Our work provides an efficient training strategy to develop accurate deep-learning interatomic potential for complex solid-state electrolyte materials, providing a promising simulation tool to accelerate solid-state battery design and applications.

摘要?利用機器學(xué)習(xí)開發(fā)精確高效的原子間勢已成為材料模擬和發(fā)現(xiàn)的一種重要方法。然而，系統(tǒng)地構(gòu)建多樣、有效的訓(xùn)練數(shù)據(jù)集仍然充滿挑戰(zhàn)。我們?yōu)?/span>Li₇La₃Zr₂O₁₂（LLZO）體系開發(fā)了一種基于深度學(xué)習(xí)的原子間勢。我們的原子間勢使用來自數(shù)據(jù)庫和第一性原理模擬的多樣化數(shù)據(jù)集進行訓(xùn)練。我們將訓(xùn)練集和測試集的覆蓋率作為訓(xùn)練迭代的收斂標(biāo)準(zhǔn)，其中覆蓋率由主成分分析計算得出。通過這一策略獲得了一個精確的LLZO原子間勢，可描述LLZO體系的結(jié)構(gòu)和動力學(xué)性質(zhì)，同時與密度泛函理論計算相比大大降低了計算成本。該原子間勢還準(zhǔn)確描述了與實驗一致的徑向分布函數(shù)和熱膨脹系數(shù)，并預(yù)測了LLZO體系由四方相到立方相的相變行為。我們的工作為開發(fā)復(fù)雜固體電解質(zhì)材料的精確深度學(xué)習(xí)原子間相互作用勢，提供了一種有效的訓(xùn)練策略，為加速固體電池的設(shè)計和應(yīng)用提供了有前景的模擬工具。