Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Anderson Acceleration of Gradient Methods with Energy for Optimization Problems

Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.

Gradient Ultra-fine Grained Surface Layer in 6063 Aluminum Alloy Obtained by Means of Rotational Accelerated Shot Peening

Gradient ultra-fine grained surface layer in 6063 aluminum alloy was obtained by means of a novel surface self-nanocrystallization technique,namely rotational accelerated shot peening(RASP)treatment.The average grain sizes along the vertical section vary from hundreds of nanometers in the top surface to micrometers in the matrix.By using orthogonal experimental design to compare roughness values and hardness values,we synthesized the processing parameters to obtain sample of smaller roughness values and higher hardness.

Design,fabrication,and cold test of an S-band high-gradient accelerating structure for compact proton therapy facility

An S-band high-gradient accelerating structure is designed for a proton therapy linear accelerator(linac)to accommodate the new development of compact,singleroom facilities and ultra-high dose rate(FLASH)radiotherapy.To optimize the design,an efficient optimization scheme is applied to improve the simulation efficiency.An S-band accelerating structure with 2856 MHz is designed with a low beta of 0.38,which is a difficult structure to achieve for a linac accelerating proton particles from 70 to 250 MeV,as a high gradient up to 50 MV/m is required.A special design involving a dual-feed coupler eliminates the dipole field effect.This paper presents all the details pertaining to the design,fabrication,and cold test results of the S-band high-gradient accelerating structure.

Ultrahigh accelerating gradient and quality factor of CEPC 650 MHz superconducting radio-frequency cavity

Two 650 MHz single-cell superconducting radio-frequency(SRF)cavities used for the Circular Electron Positron Collider(CEPC)were studied to achieve a high accelerating gradient(E_(acc))and high intrinsic quality factor(Q_(0)).The 650 MHz single-cell cavities were subjected to a combination of buffered chemical polishing(BCP)and electropolishing(EP),and their E_(acc) exceeded40 MV/m.Such a high E_(acc) may result from the cold EP with more uniform removal.BCP is easy,cheap,and rough,whereas EP is complicated,expensive,and precise Therefore,the combination of BCP and EP investigated in this study is suitable for surface treatments of mass SRF cavities.Medium temperature(mid-T)furnace baking was also conducted,which demonstrated an ultrahigh Q_(0) of 8×10^(10) at 22 MV/m for both cavities,and an extremely low BCS resistance(R_(BCS))of~1.0 nΩwas achieved a2.0 K.

Fabrication,tuning,and high-gradient testing of an X-band traveling-wave accelerating structure for VIGAS

X-band high-gradient linear accelerators are a challenging and attractive technology for compact electron linear-accelerator facilities.The Very Compact Inverse Compton Scattering Gamma-ray Source(VIGAS)program at Tsinghua University will utilize X-band high-gradient accelerating structures to boost the electron beam from 50 to 350 MeV over a short distance.A constant-impedance traveling-wave structure consisting of 72 cells working in the 2π/3 mode was designed and fabricated for this project.Precise tuning and detailed measurements were successfully applied to the structure.After 180 h of conditioning in the Tsinghua high-power test stand,the structure reached a target gradient of 80 MV/m.The breakdown rate versus gradient of this structure was measured and analyzed.

Effects of substrate-ion density gradients on light-ion acceleration from ultraintense laser pulse irradiated thin-foils

A general solution of the electrostatic potential that determines the maximum light-ion energy is derived for the test-particle acceleration model by taking into account the influence of the substrate-ion density gradient. It is shown that the substrate-ion density structure is also dependent on laser pulse duration. In the picosecond or sub-picosecond regime, the decreasing density gradient of the substrate-ions leads to an evident reduction in the acceleration efficiency of the light-ions. However, this kind of influence is negligible in the ultrashort regime.

On-chip ultrafast stackable dielectric laser positron accelerator

We present a first on-chip positron accelerator based on dielectric laser acceleration.This innovative approach significantly reduces the physical dimensions of the positron acceleration apparatus,enhancing its feasibility for diverse applications.By utilizing a stacked acceleration structure and far-infrared laser technology,we are able to achieve a seven-stage acceleration structure that surpasses the distance and energy gain of using the previous dielectric laser acceleration methods.Additionally,we are able to compress the positron beam to an ultrafast sub-femtosecond scale during the acceleration process,compared with the traditional methods,the positron beam is compressed to a greater extent.We also demonstrate the robustness of the stacked acceleration structure through the successful acceleration of the positron beam.

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

Investigation of the Acceleration Region in a Gas-Solid Co-current Down-flow Circulating Fluidized Bed

In this work, a mathematical model is established to describe the axial variation of the characteristic flow parameters (particle velocity, solid holdup and pressure gradient) in a downer. An empirical correlation is developed to estimate the particle velocity at the constant velocity section. Experimental investigations are made to validate the downer model. The model simulations have a good agreement with experimental data. Moreover, a formula is derived to predict the first acceleration section length and the whole acceleration section length.

Design and preliminary test of the LLRF in C band high-gradient test facility for SXFEL

This paper describes the design and preliminary test of the low-level radio frequency(LLRF)part of the C band high-gradient test facility for the Shanghai Soft X-ray Free-Electron Laser(SXFEL)-Linear Accelerator(LINAC).Before installation,the accelerating structures should be tested and conditioned.During the conditioning process,breakdown detection is needed to protect the accelerating structures and klystron from damage.The PCI extensions for instrumentation-based LLRF system and auto-conditioning algorithm are designed and applied in the LLRF part of the C band high-gradient test facility.Three C band accelerating structures and 1 pulse compressor have completed conditioning and were installed in the SXFEL-LINAC.

THE EFFECT OF MAGNETIC FIELDS ON LOW FREQUENCY OSCILLATING NATURAL CONVECTION WITH PRESSURE GRADIENT

The oscillating natural convection in the presence of transverse magnetic field with time depending pressure gradient is studied. The analysis of the problem is carried out by assuming that the fluid is flowing in a parallel plate configuration. The emphasis is on low frequency oscillating convective flows induced by g-jitter associated with micro gravity because of their importance to the space processing materials. A general solution for an oscillating flow in the presence of transverse magnetic field is carried out. Some special cases of the oscillating flow and its response to an applied magnetic field are performed. It was observed that the behavior of oscillating free convective flows depends on frequency, amplitude of the driving buoyancy forces, temperature gradient,magnetic field and the electric conditions of the channel walls. In the absence of magnetic field, buoyancy force plays a predominant role in driving the oscillatory flow pattern, and velocity magnitude is also affected by temperature gradients. To suppress the oscillating flow external magnetic field can be used. It is also found that the reduction of the velocity is inversely proportional to the square of the applied magnetic field with conducting wall but directly proportional to the inverse of the magnetic field with insulating wall. Detailed calculations and computational results are also carried out to depict the real situation.

The average acceleration approach applied to gravity coefficients recovery based on GOCE orbits

The average acceleration approach was applied to recover a gravity field model Model;CA from GOCE precise science orbits from September 2 to November 2, 2010, and furthermore a so called sequential least square adjustment was used. The model was compared with other gravity field models based on CHAMP, GRACE and GOCE. The result shows that the model is superior to gravity field based on CHAMP, and with higher accuracy than other international gravity field models based on only GOCE data before 80 degree. The degree geoid height of Model;CA reaches 3cm up to 90 degree and order.

An Improved Graphics Processing Unit Acceleration Approach for Three-Dimensional Structural Topology Optimization Using the Element-Free Galerkin Method

We proposed an improved graphics processing unit(GPU)acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin(EFG)method.This method can effectively eliminate the race condition under parallelization.We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model.We explored the GPU parallel algorithm of assembling stiffness matrix,solving discrete equation,analyzing sensitivity,and updating design variables in detail.We also proposed a node pair-wise method for assembling the stiffnessmatrix and a node-wise method for sensitivity analysis to eliminate race conditions during the parallelization.Furthermore,we investigated the effects of the thread block size,the number of degrees of freedom,and the convergence error of preconditioned conjugate gradient(PCG)on GPU computing performance.Finally,the results of the three numerical examples demonstrated the validity of the proposed approach and showed the significant acceleration of structural topology optimization.To save the cost of optimization calculation,we proposed the appropriate thread block size and the convergence error of the PCG method.

Structure and material study of dielectric laser accelerators based on the inverse Cherenkov effect

Dielectric laser accelerators(DLAs)are considered promising candidates for on-chip particle accelerators that can achieve high acceleration gradients.This study explores various combinations of dielectric materials and accelerated structures based on the inverse Cherenkov effect.The designs utilize conventional processing methods and laser parameters currently in use.We optimize the structural model to enhance the gradient of acceleration and the electron energy gain.To achieve higher acceleration gradients and energy gains,the selection of materials and structures should be based on the initial electron energy.Furthermore,we observed that the variation of the acceleration gradient of the material is different at different initial electron energies.These findings suggest that on-chip accelerators are feasible with the help of these structures and materials.

基于FEM的引力参考传感器自引力计算与补偿

空间引力波探测太极计划将利用激光干涉的方法,测量两个检验质量之间的距离变化反演引力波信息。在0.1 mHz处,要求检验质量在敏感轴方向的总残余加速度保持在3×10^(-15)m·s^(-2)/√Hz以下。由航天器载荷静引力、热形变和质量波动引起的自引力噪声是检验质量的残余加速度噪声主要来源之一,要求检验质量在敏感轴方向的自引力加速度小于1×10^(-10)m/s^(2),引力梯度小于5×10^(-8)s^(-2)。为了计算检验质量处的自引力大小和引力梯度,针对检验质量与引力源几何形状的不规则性,基于有限元法编写程序计算了引力参考传感器中的引力源作用在检验质量上的线加速度、角加速度和引力梯度。为了缩短计算时间,提出“类自适应”网格划分方法以减小网格数量,并设计了配重以补偿自引力。计算结果显示,经过补偿后的检验质量在敏感轴方向的自引力加速度为9.2377×10^(-12)m/s^(2),引力梯度为-2.5691×10^(-8)s^(-2),满足设计要求。本研究能够为航天器和引力参考传感器的设计与引力补偿提供参考与指导。

求解一类非光滑凸优化问题的相对加速SGD算法

一阶优化算法由于其计算简单、代价小,被广泛应用于机器学习、大数据科学、计算机视觉等领域,然而,现有的一阶算法大多要求目标函数具有Lipschitz连续梯度,而实际中的很多应用问题不满足该要求。在经典的梯度下降算法基础上,引入随机和加速,提出一种相对加速随机梯度下降算法。该算法不要求目标函数具有Lipschitz连续梯度,而是通过将欧氏距离推广为Bregman距离,从而将Lipschitz连续梯度条件减弱为相对光滑性条件。相对加速随机梯度下降算法的收敛性与一致三角尺度指数有关,为避免调节最优一致三角尺度指数参数的工作量,给出一种自适应相对加速随机梯度下降算法。该算法可自适应地选取一致三角尺度指数参数。对算法收敛性的理论分析表明,算法迭代序列的目标函数值收敛于最优目标函数值。针对Possion反问题和目标函数的Hessian阵算子范数随变量范数多项式增长的极小化问题的数值实验表明,自适应相对加速随机梯度下降算法和相对加速随机梯度下降算法的收敛性能优于相对随机梯度下降算法。

基于鲁棒控制的自适应分数阶梯度优化算法设计

当目标函数是强凸函数时,一般的分数阶梯度下降法不能够使函数收敛到最小值点,只能收敛到一个包含最小值点的区域内或者是发散的.为了解决这个问题,本文提出了自适应分数阶梯度下降法(AFOGD)和自适应分数阶加速梯度下降法(AFOAGD)两种新的优化算法.受到鲁棒控制理论中二次约束和李雅普诺夫稳定性理论的启发,建立了一个线性矩阵不等式去分析所提出的算法的收敛性.当目标函数是L-光滑且m-强凸时,算法可以达到R线性收敛.最后几个数值仿真证明了算法的有效性和优越性.

C波段高梯度加速结构样机研制

本文介绍了C波段高梯度加速结构研制的内容,通过采用低群速度、4π/5工作模式、等梯度结构、拱形腔和大束流孔径设计方法、创造性的内水冷可调谐腔体结构、悬挂式焊接方法等技术,实现了国内第一支C波段高梯度加速结构段的工程应用,在束流试验中获得了50.8 MV/m的世界最高C波段带束加速梯度。

一种基于稀疏优化和Nesterov动量策略的模型剪枝算法

随着深度学习快速发展,模型的参数量和计算复杂度爆炸式增长,在移动终端上部署面临挑战,模型剪枝成为深度学习模型落地应用的关键。目前,基于正则化的剪枝方法通常采用L2正则化并结合基于数量级的重要性标准,是一种经验性的方法,缺乏理论依据,精度难以保证。受Proximal梯度方法求解稀疏优化问题的启发,本文提出一种能够在深度神经网络上直接产生稀疏解的Prox⁃NAG优化方法,并设计了与之配套的迭代剪枝算法。该方法基于L1正则化,利用Nesterov动量求解优化问题,克服了原有正则化剪枝方法对L2正则化和数量级标准的依赖,是稀疏优化从传统机器学习向深度学习的自然推广。在CIFAR10数据集上对ResNet系列模型进行剪枝实验,实验结果证明Prox⁃NAG剪枝算法较原有剪枝算法性能有所提升。