Heavy-Ball型动量方法的最优个体收敛速率

动量方法作为一种加速技巧被广泛用于提高一阶梯度优化算法的收敛速率.目前,大多数文献所讨论的动量方法仅限于Nesterov提出的加速方法,而对Polyak提出的Heavy-ball型动量方法的研究却较少.特别,在目标函数非光滑的情形下,Nesterov加速方法具有最优的个体收敛性,并在稀疏优化问题的求解中具有很好的效果.但对于Heavy-ball型动量方法,目前仅仅获得了平均输出形式的最优收敛速率,个体收敛是否具有最优性仍然未知.对于非光滑优化问题,通过巧妙地设置步长,证明了Heavy-ball型动量方法具有最优的个体收敛速率,从而说明了Heavy-ball型动量方法可以将投影次梯度方法的个体收敛速率加速至最优.作为应用,考虑了l1范数约束的hinge损失函数优化问题.通过与同类的优化算法相比,实验验证了该理论分析的正确性以及所提算法在保持稀疏性方面的良好性能.

A Study on the Convergence of Gradient Method with Momentum for Sigma-Pi-Sigma Neural Networks

In this paper, a gradient method with momentum for sigma-pi-sigma neural networks (SPSNN) is considered in order to accelerate the convergence of the learning procedure for the network weights. The momentum coefficient is chosen in an adaptive manner, and the corresponding weak convergence and strong convergence results are proved.

基于AdaBelief的Heavy-Ball动量方法

同时使用动量和自适应步长技巧的自适应矩估计(Adaptive Moment Estimation,Adam)型算法广泛应用于深度学习中.针对此方法不能同时在理论和实验上达到最优这一问题,文中结合AdaBelief灵活调整步长提高实验性能的技巧,以及仅采用指数移动平均(Exponential Moving Average,EMA)策略调整步长的Heavy-Ball动量方法加速收敛的优点,提出基于AdaBelief的Heavy-Ball动量方法.借鉴AdaBelief和Heavy-Ball动量方法收敛性分析的技巧,巧妙选取时变步长、动量系数,并利用添加动量项和自适应矩阵的方法,证明文中方法对于非光滑一般凸优化问题具有最优的个体收敛速率.最后,在凸优化问题和深度神经网络上的实验验证理论分析的正确性,并且证实文中方法可在理论上达到最优收敛性的同时提高性能.

基于AdaGrad+的自适应Heavy-Ball动量法及其最优个体收敛性

自适应策略与动量法是提升优化算法性能的常用方法。目前自适应梯度方法大多采用AdaGrad型策略,但该策略在约束优化中效果不佳,为此,研究人员提出了更适用于处理约束问题的AdaGrad+方法,但其与SGD一样在非光滑凸情形下未达到最优个体收敛速率,结合NAG动量也并未达到预期的加速效果。针对上述问题,文中将AdaGrad+调整步长的策略与Heavy-Ball型动量法加速收敛的优点相结合,提出了一种基于AdaGrad+的自适应动量法。通过设置加权动量项、巧妙选取时变参数和灵活处理自适应矩阵,证明了该方法对于非光滑一般凸问题具有最优个体收敛速率。最后在l∞∞范数约束下,通过求解典型的hinge损失函数优化问题验证了理论分析的正确性,通过深度卷积神经网络训练实验验证了该方法在实际应用中也具有良好性能。

Solution to the Dirac equation using the finite difference method

In this study,single-particle energy was examined using the finite difference method by taking 208Pb as an example.If the first derivative term in the spherical Dirac equation is discretized using a three-point formula,a one-to-one correspondence occurs between the physical and spurious states.Although these energies are exactly the same,the wave functions of the spurious states exhibit a much faster staggering than those of the physical states.Such spurious states can be eliminated when applying the finite difference method by introducing an extra Wilson term into the Hamiltonian.Furthermore,it was also found that the number of spurious states can be reduced if we improve the accuracy of the numerical differential formula.The Dirac equation is then solved in a momentum space in which there is no differential operator,and we found that the spurious states can be completely avoided in the momentum space,even without an extra Wilson term.

A numerical method of combined SPF-MEM-LBM on the rockfall-induced surge and its application

Rockfalls in reservoirs are prone to induce surges, posing a severe threat to passing vessels and facilities. A scheme combined Single-phase freesurface method(SPF), momentum exchange method(MEM), and Lattice Boltzmann method(LBM) is proposed to predict the impact of rockfall-induced surges. First, the LBM-SPF model is used to simulate the motion of the free surface, and the MEM model is used to calculate the hydrodynamic force acting on rock mass. To address the incompatibility issue arising from the coupling of LBM-SPF model and MEM model, a correction scheme inside the solid is induced. The simulation results of the single particle and double particle sedimentation in cavity show the feasibility and accuracy of the method designed in this paper. Moreover, the validation experiments of Scott Russel’s wave generator show that the proposed scheme can simulate wave profile stably. The simulation results emphasize that the waves induced by rockfalls have a significant impact on the safe operation of the Laxiwa dam and the passing vessels in the reservoir.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Upshot of ohmically dissipated Darcy-Forchheimer slip flow of magnetohydrodynamic Sutterby fluid over radiating linearly stretched surface in view of Cash and Carp method

The present work concerns the momentum and heat transmission of the electro-magnetohydrodynamic (E-MHD) boundary layer Darcy-Forchheimer flow of a Sutterby fluid over a linear stretching sheet with slip. The nonlinear equations for the proposed model are analyzed numerically. Suitable techniques are used to transform the coupled nonlinear partial differential equations (PDEs) conforming to the forced balance law, energy, and concentration equations into a nonlinear coupled system of ordinary differential equations (ODEs). Numerical solutions of the transformed nonlinear system are obtained using a shooting method, improved by the Cash and Carp coefficients. The influence of important physical variables on the velocity, the temperature, the heat flux coefficient, and the skin-friction coefficient is verified and analyzed through graphs and tables. From the comprehensive analysis of the present work, it is concluded that by intensifying the magnitude of the Hartmann number, the momentum distribution decays, whereas the thermal profile of fluid increases. Furthermore, it is also shown that by aug- menting the values of the momentum slip parameter, the velocity profile diminishes. It is found that the Sutterby fluid model shows shear thickening and shear thinning behaviors. The momentum profile shows that the magnitude of velocity for the shear thickening case is dominant as compared with the shear thinning case. It is also demonstrated that the Sutterby fluid model reduces to a Newtonian model by fixing the fluid parameter to zero. In view of the limiting case, it is established that the surface drag in the case of the Sutterby model shows a trifling pattern as compared with the classical case.

Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism(MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed,and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust.More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.

Electron momentum spectroscopy of NF_3

The electronic structure of nitrogen trifluoride was investigated by combining the high-resolution electron momentum spectroscopy with the high-level calculations. The experimental binding energy spectra and the momentum distributions of each orbital were compared with the results of Hartree-Fock, density functional theory （DFT）, and symmetry-adapted- cluster configuration-interaction （SAC-CI） methods. SAC-CI and DFT-B3LYP with the aug-cc-pVTZ basis set can well reproduce the binding energy spectra and the observed momentum distributions of the valence orbitals except 1 a2 and 4e orbitals. It was found that the calculated momentum distributions using DFT-B3LYP are even better than those using the high-level SAC-CI method.

Experimental and Theoretical Investigation of the Valence Orbital Binding Energy Spectra and Momentum Distributions of C_(4)H_(10) Molecule

The C_(4)H_(10) molecule has been studied by high resolution(e,2e)spectrometer at a total energy of 1200eV and using symmetric non-coplanar kinematics.The binding energy spectra ranging up to 32eV are measured at out-of-plane azimuthal angles from 0° to 22° corresponding to target electron momentum from about 0.1 to 1.8 a.u.The binding energy spectra and electron momentum distributions obtained for the valence orbitals are compared with the theoretical result calculated by using restricted Hartree-Fock and density functional theory methods.The agreement between theory and experiment of orbital electron momentum distributions is generally good.

Tower-based observation of air-sea momentum flux:comparisons between onshore and offshore winds

We investigate the air-sea momentum flux in the marine atmospheric boundary layer using a tower-based direct measurement method.First,we compare the collected data with previous observations,and the results are roughly consistent.Next,in the low-to-moderate winds,the exchange coefficients(or drag coefficients)deviate between onshore and offshore winds,which exhibits the influence of surface wave on the momentum flux.Furthermore,we use a surface-wave-involved parameterization scheme to explain the dependence of momentum flux on surface wave.The results consolidate the influence of surface wave on momentum flux on the one hand,and validate the surface-wave-involved parameterization scheme on the other hand.

Electron Momentum Density and X-ray Structure Factors of Fcc-Copper

In this paper, we report the ground state properties i.e. electron momentum density and X-ray structure factors of fcc-copper are presented. The Am241 Compton spectrometer, which uses 59.54 keV gamma-rays, has been used for the Compton profile measurement. To compare the experimental data, the Compton profiles within the framework of linear combination of atomic orbitals (LCAO) method using Hartree–Fock (HF), density functional (DF) and hybrid B3PW schemes embodied in the CRYSTAL06 code have been computed. Among the various theoretical calculations, it is found that the present experimental data is in very good agreement with the hybrid B3PW scheme. A real-space analysis of the experimental Compton profile shows the metal-like behavior of copper The structure factors for copper are computed using hybrid B3PW scheme and compared with available experimental and theoretical data.

高阶轨道角动量传输光纤设计及传输特性研究(内封底文章)

为解决一般轨道角动量传输光纤传输轨道角动量模式数量少、质量差的问题,提出了一种基于正六边形空气孔排列的新型光子晶体光纤结构。该光纤引入了空气填充率高的矩形空气孔以及采用高折射率材料填充环形传输区域,能够有效提高环形传输区域和包层间的折射率差,且正六边形排列空气孔有利于提高模间有效折射率差。经过结构优化得到最优光纤结构,有限元法的分析结果表明,最优结构下,该光纤在常用波段S+C+L+U波段上能够支持142种轨道角动量模式的传输,最高阶数达到36阶。且所提出光纤具有良好的传输特性,本征模式的最高限制性损耗为10−9 dB/m量级,与典型轨道角动量传输光子晶体光纤相比至少降低了一个数量级;最大有效模场面积能够达到206.18μm^(2),最小非线性系数低至0.397 W^(−1)∙km^(−1);色散平坦且最小色散变化低至1.4578 ps/(nm∙km);所有本征模式纯度均在93.4%~96.8%范围内。且该光纤具有较好的制备可行性,对制造精度要求不高。因此,该光纤在基于轨道角动量光纤的复用系统中具有广阔的应用前景,为提高通信容量提供了一种有效手段。

基于加速无约束张量隐因子分解模型的Web服务Qo S估计

针对基于张量非负隐因子分解模型的Web服务QoS估计方法过于依赖非负初始随机数据以及特意设计的非负训练方法,导致模型的兼容性和扩展性不高的问题,提出了加速无约束张量隐因子分解模型。其主要思想包括三部分:将非负性约束从决策参数转移到输出的隐因子,并通过单元素映射函数连接它们;运用结合动量方法的随机梯度下降算法,有效提高模型的收敛速度与估计精度;给出加速无约束张量隐因子分解模型的详细算法和结果分析。在实际工业应用中的2个动态QoS数据集上的实证研究表明,与最先进的QoS估计模型相比,所提模型具有较高的计算效率和估计精度。

掺混含氧燃料对混合燃料喷射特性的影响研究

为探究添加含氧燃料对燃料喷射特性的影响,将体积分数均为50%的聚甲氧基二甲醚(PODE)和正丁醇掺混于柴油制得PODE-柴油混合燃料和正丁醇-柴油混合燃料,标记为P50和B50。在高压共轨试验台上使用基于冲量法的喷射特性测试系统,研究了柴油、PODE-柴油混合燃料、正丁醇-柴油混合燃料三种燃料在多种工况下的喷射特性差异。结果表明,掺混含氧燃料对喷油速率有较大的影响:P50的体积流量小于柴油,而质量流量则相反;B50和柴油的喷油速率在低压下差异很小,但当压力升高至130 MPa时,二者的喷油速率差异明显;相同脉宽及喷射压力时与柴油相比,循环喷油量以体积计,B50大于柴油且差距随压力上升而增大,而P50则低于柴油且差距随压力上升而缩小;循环喷油量以质量计,P50和B50均高于柴油且差异率随压力上升而增大,但B50和柴油差异率的上升幅度比P50小;以喷射能量计,除小脉宽工况外,B50和P50的喷射能量均小于柴油,喷射能量由大到小排序为柴油、B50、P50。

带消极动量的自适应步长随机方差缩减方法

近年来,随机方差缩减类方法在解决大规模机器学习问题中取得很大成功,自适应步长技术的引入减轻了该类方法的调参负担。针对自适应步长的方差缩减算法SVRG-BB,指出其算法设计带来了“进展-自适应步长有效性”的权衡问题。因此引入Katyusha动量以更好地处理该权衡问题,并且在强凸假设下证明由此得到的SVRG-BB-Katyusha算法的线性收敛性质。之后基于“贪婪”思想,提出稀疏地使用Katyusha动量的SVRG-BB-Katyusha-SPARSE算法。在公开数据集上的数值实验结果表明,提出的2个改进算法较SVRG-BB有较稳定的优势,即在达到一定外循环数时优化间隙有若干个数量级的减小。

基于改进BP神经网络的网络流量预测

传统网络流量预测方法常面临精度不足、时间复杂度高的问题,且在处理复杂的网络流量时,难以达到理想的预测效果。为克服这些挑战,采用深度学习中的反向传播(Back Propagation,BP)神经网络算法,并结合改进的梯度下降法,通过引入动量项与变步长法相结合的方式,有效降低误差值,实现了对网络流量的准确预测。该方法旨在更好地满足用户需求,优化网络性能,并提升网络服务质量。实验结果表明,改进后的BP神经网络算法在网络流量预测中展现出良好的可行性与稳健性,同时达到了较高的预测精度。

声势律动教学法在初中音乐教学中的应用策略探究

声势律动教学法应用在初中音乐教学中,有助于激发学生的学习兴趣,激活学生的创新思维,提高学生的音乐素养,有助于提高音乐课堂教学效率。文章以人教版初中音乐教材中的相关案例为主要素材,从导入环节、节奏训练、听觉练习、作品鉴赏以及音乐创编等方面,探究声势律动教学法在音乐教学中的应用策略,以此优化音乐教学形式,提高音乐教学效率以及学生的音乐学科核心素养。

喷水推进器推力的动量计算法

介绍了喷水推进理论,把复杂的喷水推进系统分解成两个主要部件泵体和进水管道进行研究,着重考虑了船体边界层对进口动量和来流动能的影响,并用数学方法表示了这些影响.其次,基于动量守恒和能量守恒,从理论上建立推力与功率、航速的关系式,并用此公式对某喷水推进船的推力进行计算,计算结果和试验曲线能很好地吻合.分析了本计算方法可能出现的误差.