|Alternative Title||Efficiency and reliability of the minimization method in molecular simulations|
|Place of Conferral||北京|
（一）研究了初始构型、极值方法类型和收敛条件对准静态分子模拟计算效率和可靠性的影响。结果表明，每个加载步的初始构型不仅对计算效率产生显著影响，也会改变原子键的断裂以及微结构的演化。初始构型的获得与加载方式密切相关，对加载过程中原子势阱演化规律的研究表明，基于弹性变形的映射加载方式可以有效提高计算效率。通过考察六种不同类型的极值方法在结构驰豫和位错演化计算中的效率，发现共轭梯度（CG）法的综合性能最佳，BB方法在结构驰豫中收敛效率比有限内存的拟牛顿方法（Limited-memory BFGS, LBFGS）更高，而FIRE算法收敛性能很差。通过研究收敛准则和收敛阈值对模拟计算效率和可靠性的影响，指出不同收敛准则的特点，为具体应用中收敛参数的选择提供了指导和建议。
（二）研究了积分格式和监视器对FIRE方法在准静态分子模拟中收敛性能的影响。首先，采用不同积分格式的FIRE方法进行不同类型分子模拟的研究，发现向前欧拉（Forward Euler, FE）积分的计算效率最低；半隐式欧拉（Semi-implicit Euler, SE）积分采用激进的更新方式，加速效果最好，但是容易在位错演化中出现不收敛的情况；Velocity Verlet (VV)积分的计算效率略低于SE，但收敛性好于SE。因此，积分格式对FIRE的加速效果有显著影响，这一结论不同于文献中认为的没有影响的观点。其次，针对SE积分格式不收敛的问题，提出在FIRE方法中使用能量监视器，相比原有的功率监视器，采用能量监视器的SE积分格式能在保留高计算效率、低内存占用的前提下，又具有良好的收敛性。针对多个体系的计算结果表明，FIRE方法采用能量监视器和SE积分是进行一般准静态模拟的最佳选择，而采用功率监视器和SE积分则具有临界事件分析能力。最后，通过将FIRE方法应用到单晶铜三维纳米压入和石墨烯结构驰豫的模拟中，发现FIRE方法对于偏“硬”的金属材料力学性能计算有较高的计算效率，而对于偏“软”的材料其计算能力仍需要作进一步改进。
Development of micro/nano mechanics requires new molecular simulation methods that could deal with lager systems in order to study some key mechanical problems with higher efficiency and fidelity. The minimization method, as the core procedure of molecular statics (MS) and multi-scale approaches, has been widely used in quasi-static mechanical analysis of micro/nano structures. Efficiency of the minimization method determines the maximum simulation scale in these applications. Therefore, investigating the efficiency and reliability of minimization methods in molecular simulations could not only uncover the mechanisms that govern the efficiency limit but also provide guidelines for developing new high-efficiency simulation methods. In this work, minimization methods with different algorithms are applied to serval typical mechanical problems in nanoscale. Factors that affect the efficiency and reliability of the algorithms are studied systematically. Based on the study, accelerated algorithms and strategies are proposed. The main results and conclusions are as follows:
(1) Influence of the initial configuration, optimization algorithm and convergence condition on the efficiency and fidelity of minimization method is investigated. It is found that initial configurations obtained from different loading operations have severe influence on the efficiency of minimization method in simulations of molecular system with bond-breaking events and dislocation evolutions. Analysis of energy landscape evolutions indicates that the mapping-style loading operation usually generates initial configurations very close to the final states, so it shows much higher efficiency than the direct loading operation. Minimization methods with six different optimization algorithms are applied to two typical molecular simulation cases: structural relaxation and dislocation propagation. The Barzilai-Borwein algorithm (BB) shows the fastest convergence in the case of structural relaxation, while the Limited-memory BFGS algorithm (LBFGS) is the fastest one in simulation of dislocation propagation. The FIRE algorithm shows poor efficiency in both cases which is not as fast as reported in other papers. By considering memory consumptions and convergence rate, the results suggest that the conjugate gradient (CG) algorithm should be the first choice in large-scale molecular simulations. Influence of convergence control algorithms on the efficiency and reliability of minimization method in molecular simulations are also studied. Based on the simulation results, practical guidelines for choosing convergence algorithm and conditions are discussed accordingly.
(2) Effects of integration formula and state monitor on the performance of FIRE method used in molecular simulations are studied. It is found that performance of the Forward Euler (FE) integration is always the worst in all the simulation cases. The Semi-implicit Euler (SE) integration with aggressive strategy shows the fastest convergence speed, while the Velocity Verlet (VV) integration is slightly slower than SE but can reach to lower energy states. The conclusion of integration-dependent performance of the FIRE method is different from that of the other reports. In order to ensure the convergence of SE integration, an energy monitor with less memory usage is proposed. Further simulation results indicate that SE integration with the energy monitor is the best choice for quasi-static molecular simulations. Applications of the FIRE method to three-dimensional nanoindentation and relaxation of warping graphene reveals that it has higher efficiency on relaxing “hard” materials but lower efficiency for “soft” materials.
(3) Accelerated algorithms and strategies based on macro mechanics knowledge are proposed for molecular simulation of several typical deformation modes: (i) Inertia accelerated molecular statics (IAMS) method is put forward based on characteristics of atomic motions at adjacent steps. By learning from previous minimization process, IAMS maps initial configuration to the state close to final energy minimum which let it be at least 10 times faster than ordinary MS method. (ii) Accelerated dislocation propagation method is designed for edge dislocation evolution in the simple shear model. In the new algorithm, computational cost of dislocation propagation is independent of model size. (iii) Partition minimization algorithm with and without mapping are built for the simulation of inital dislocation evolution in nanoindentation. Results show promising efficiency improvement by reducing the cost of dislocation propagation. (iv) Algorithm combining potential minimizing and free energy minimization is proposed to improve computational efficiency of molecular statistical thermodynamics (MST) method for quasi-static analysis of nanostructures at finite temperature.
(4) The comparative simulations of dislocation evolution in nanoindentation are carried out in terms of both molecular dynamics (MD) and molecular stataics (MS) methods, to explore what really govern the computational efficiency and fidelity in molecular simulations relevant to dislocation evolutions. It is found that although all simulations can present similar relationship between indentation force and depth, there still might be some significant differences in the simulated dislocation patterns and computational efficiency. Firstly, the MS simulations show more complicated dislocations. Secondly, the necessary computational effort of MS increases nonlinearly with indentation depth, compared to the linear dependence in MD simulations. More importantly, it is revealed that the time consumption of the minimization iteration is strongly dependent on the moving of dislocation loops and increases greatly when dislocation loops move long distances. Whereas MD simulations of complicated dislocations patterns may need less time cost but present immature dislocation evolutions, since the relaxation steps in MD simulations are fixed beforehand, regardless of the dislocation loops moving to equilibrium state or not. Dislocation quantitative analysis shows that the reasonable description of dislocation density within the plastic zone is the necessary factor for nanoindentation simulations, which can be used to help select the proper convergence threshold in MS or relaxation time in MD to trade off between efficiency and accuracy.
(5) Two accelerated algorithms are put forward particularly for molecular simulation of large-scale nanoindentation. Firstly, the limited-iteration molecular statics (LIMS) which combines advantages of MS and MD is proposed. Specifically, it takes advantage of MS with quick convergence for elastic deformation and localized dislocation events, and MD with limited iteration steps for dislocation loops propagation As a result, LIMS shows sub-linear computational cost in nanoindentation simulations. Secondly, the removing separated dislocation loop (RSDL) algorithm is constructed. By removing dislocation loops at a specific location, the long-range propagation of dislocation loops as well as non-physical interactions between the plastic zone and artificial boundaries is avoid in the RSDL algorithm, so the computation cost can be dramatically reduced. It shows 8 times higher efficiency by introducing the RSDL in MS simulations. Moreover, it is expected that the RSDL could be utilized in multi-scale methods to deal with growing atomic regions due to dislocation evolution in order to improve efficiency.
|双飞. 极值方法在分子模拟中的计算效率和可靠性研究[D]. 北京. 中国科学院大学,2018.|
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