基于机器学习原子势函数的原子动力学蒙特卡洛程序TensorKMC的优化

Optimization of Atomic Kinetics Monte Carlo Program TensorKMC Based on Machine Learning Atomic Potential Functions

核反应堆压力容器是核电站中最重要的部件之一,在使用过程中通常会受到辐照损伤,这极大影响了其使用寿命,给核电站的安全带来隐患。原子动力学蒙特卡洛方法(AKMC)是研究材料辐照损伤的有效理论方法,可以与计算机数值模拟进行结合来研究压力容器的微结构演变。辐照损伤的材料存在缺陷,原子间相互作用建模时需要考虑非球对称相互作用,但TensorKMC在计算时并没有考虑到原子的角向作用。文中针对该问题,提出了一种包含角向相互作用、可以与TensorKMC的三重编码完美结合的指纹建模方法,并可利用多重度对角向指纹的计算过程进行化简。文中在TensorKMC程序中实现了该方法,测试结果显示角向指纹对势函数的精度有显著影响,最大角动量越高,势函数越精准,程序的模拟耗时也会显著增加。同时,也针对TensorKMC的原子势函数的激活函数开展了测试,结果表明梯度光滑的Softplus和SquarePlus相比初版TensorKMC所用的ReLU在拟合高维势能面时有明显的优势,在最大角动量较低时ReLU有性能优势,但随着最大角动量的增大,不同激活函数对总体模拟时间几乎无特别影响。因此,在实际研究中推荐使用梯度光滑的激活函数。

The nuclear reactor pressure vessel is a crucial component in a nuclear power plant,but it is susceptible to damage from irradiation during its use.This damage greatly affects its service life and poses a potential safety hazard.The atomic kinetics Monte Carlo(AKMC)method is an effective theoretical method for studying the irradiation damage of materials.It can be combined with numerical computer simulations to study the microstructural evolution of pressure vessels.Since irradiated damaged materials have defects,the modeling of interatomic interactions must consider non-spherical symmetric interactions.However,the TensorKMC method does not account for the angular interactions of atoms in its calculations.To address this issue,this paper proposes a fingerprint modeling method that includes angular interactions.It can be perfectly combined with the triple encoding of TensorKMC,and the computational process of angular fingerprinting can be simplified by using multiple weight.We have implemented this method in the TensorKMC program.The test results show that the angular fingerprint has a significant impact on the accuracy of the potential function.The higher the maximum angular momentum,the more accurate the potential function is.However,the simulation time consumed by the program will increase significantly.We also test the activation functions for the atomic potential function of TensorKMC.The results show that the gradient-smooth Softplus and SquarePlus have a significant advantage over the ReLU used in the initial version of TensorKMC in fitting the high-dimensional potential surface.The ReLU has a performance advantage at low maximum angular momentum,but as the maximum angular momentum increases,the different activation functions have almost no particular effect on the overall simulation time.Therefore,we recommend using gradient-smooth activation functions in practical studies.