物理学报2024，Vol.73Issue(16)：22-29,8.DOI:10.7498/aps.73.20240852
基于数值稳定型神经网络的Villain-Lai-Das Sarma方程的动力学标度行为研究
Study on dynamic scaling behavior of Villain-Lai-Das Sarma equation based on numerically stable nueral networks
摘要
Abstract
The Villain-Lai-Das Sarma(VLDS)equation has received much attention in surface growth dynamics due to its effective description of molecular beam epitaxy(MBE)growth process.However,the scaling exponent of the VLDS equation driven by long-range correlated noise is still unclear,because different analytical approximation methods yield inconsistent results.The nonlinear term in the VLDS equation challenges the numerical simulation methods,which often leads to the problem of numerical divergence.In the existing numerical approaches,the exponential decay techniques are mainly used to replace nonlinear terms to alleviate the numerical divergence.However,recent studies have shown that these methods may change the scaling exponent and universality class of the growth system.Therefore,we propose a novel deep neural network-based method to address this problem in this work.First,we construct a fully convolutional neural network to characterize the deterministic terms in the VLDS equation.To train the neural network,we generate training data by using the traditional finite-difference method before numerical divergence occurs.Then,we train the neural network to represent the deterministic terms,and perform simulations of VLDS driven by long-range temporally and spatially correlated noises based on the neural networks.The simulation results demonstrate that the deep neural networks constructed here possess good numerical stability.It can obtain reliable scaling exponents of the VLDS equation driven by different uncorrelated noise and correlated noise.Furthermore,in this work,it is also found that the VLDS system driven by long-range correlated noise exhibits a mound-like morphology when the temporal correlation exponent is large enough,while the growing surface morphology driven by spatially correlated noise still presents a self-affine fractal structure,independent of the spatial correlation exponent.关键词
神经网络/分子束外延生长/Villain-Lai-Das Sarma方程/动力学标度Key words
neural network/molecular beam epitaxy growth/Villain-Lai-Das Sarma equation/dynamic scaling引用本文复制引用
宋天舒,夏辉..基于数值稳定型神经网络的Villain-Lai-Das Sarma方程的动力学标度行为研究[J].物理学报,2024,73(16):22-29,8.基金项目
中央高校基本科研业务费专项资金(批准号:2024QN11021)资助的课题. Project supported by the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.2024QN11021). （批准号:2024QN11021）
