近年來(lái)機(jī)器學(xué)習(xí)（ML）的快速發(fā)展使得基于第一性原理計(jì)算高效獲得高精度分子動(dòng)力學(xué)力場(chǎng)成為可能。目前人們已經(jīng)發(fā)展了許多機(jī)器學(xué)習(xí)的力場(chǎng)模擬方法，由此實(shí)現(xiàn)了眾多分子和固態(tài)系統(tǒng)的高精度計(jì)算，其精度接近密度泛函理論（DFT）等的量子力學(xué)方法，同時(shí)計(jì)算量顯著降低。然而，當(dāng)前大多數(shù)可用的ML力場(chǎng)只能給出能量、力和應(yīng)力點(diǎn)的估算，而不是預(yù)測(cè)性分布，因而不能顯示模型的不確定性。若沒(méi)有模型不確定性估算，力場(chǎng)的擬合將費(fèi)時(shí)費(fèi)力，即需要從第一性原理計(jì)算數(shù)據(jù)庫(kù)中手動(dòng)或隨機(jī)選擇數(shù)千個(gè)參考結(jié)構(gòu)來(lái)擬合。另外，在分子動(dòng)力學(xué)模擬中，由于缺乏對(duì)模型不確定性的評(píng)估方法，將難以確定力場(chǎng)何時(shí)是可信賴的，從而導(dǎo)致結(jié)果的不可靠。

來(lái)自美國(guó)哈佛大學(xué)的Jonathan Vandermause和Boris Kozinsky共同領(lǐng)導(dǎo)的團(tuán)隊(duì)報(bào)道了一種基于機(jī)器學(xué)習(xí)的力場(chǎng)構(gòu)建方法。該方法基于高斯過(guò)程回歸的主動(dòng)學(xué)習(xí)框架發(fā)展。其優(yōu)勢(shì)有二：其一，可以基于密度泛函理論（DFT）計(jì)算獲得小數(shù)據(jù)集（~100個(gè)）來(lái)獲得精確的力場(chǎng)；其二，通過(guò)誤差估計(jì)可在偏離訓(xùn)練數(shù)據(jù)時(shí)自動(dòng)進(jìn)化。該優(yōu)勢(shì)使得該方法可以準(zhǔn)確模擬和捕捉那些短暫且發(fā)生概率較低的原子事件。這些優(yōu)勢(shì)源于該模型使用了完全可解釋的、低維的、非參數(shù)化力場(chǎng)。與經(jīng)典的Stillinger-Weber力場(chǎng)類似，本研究使用的力場(chǎng)是基于多體原子間相互作用的，通常在2體和3體模型下即可具有足夠的精度?；诖耍蓪⒚枋龇臻g簡(jiǎn)化為一個(gè)低維空間，這一方面使得通過(guò)一組小的訓(xùn)練數(shù)據(jù)即可對(duì)全空間進(jìn)行采樣，另一方面也簡(jiǎn)化了學(xué)習(xí)任務(wù)，從而可以采用數(shù)據(jù)驅(qū)動(dòng)的方式實(shí)現(xiàn)參數(shù)的自動(dòng)調(diào)整。將該方法應(yīng)用于含有單一或多種元素體系的分子動(dòng)力學(xué)模擬，如鋁晶體熔化、空位擴(kuò)散和原子擴(kuò)散、AgI中離子擴(kuò)散等。結(jié)果表明，他們的方法能以低幾個(gè)數(shù)量級(jí)的計(jì)算成本獲得與DFT計(jì)算相當(dāng)?shù)木?，目前已完全在線開(kāi)源發(fā)布。

On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events

Jonathan Vandermause， Steven B. Torrisi， Simon Batzner， Yu Xie， Lixin Sun， Alexie M. Kolpak & Boris Kozinsky

Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations， which can result in low training efficiency and unpredictable errors when applied to structures not represented in the training set of the model. This severely limits the practical application of these models in systems with dynamics governed by important rare events， such as chemical reactions and diffusion.We present an adaptive Bayesian inference method for automating the training of interpretable， low-dimensional， and multi-element interatomic force fields using structures drawn on the fly from molecular dynamics simulations.Within an active learning framework， the internal uncertainty of a Gaussian process regression model is used to decide whether to accept the model prediction or to perform a first principles calculation to augment the training set of the model.The method is applied to a range of single- and multi-element systems and shown to achieve a favorable balance of accuracy and computational efficiency， while requiring a minimal amount of ab initio training data.We provide a fully open-source implementation of our method， as well as a procedure to map trained models to computationally efficient tabulated force fields.
責(zé)任編輯:pj