Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

Partial Ordering of Range Symmetric Matrices and M-Projectors with Respect to Minkowski Adjoint in Minkowski Space

In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].

Adaptive broadband beamformer for nonuniform linear array based on second order cone programming

Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.

ATOMIC ORDERING AND DISORDERING OF INTERMETALLIC PHASES

All intermetallic phases have a tendency to atomic long-range ordering, according to the ordering energy, they may be permanently ordered (up to the melting-point) or reversibly ordered (up to a critical temperature). The paper considers ways of disordering intermetallic phases, in relation to the ordering energy and diffusivities, and some properties of partially ordered intermetallic phases (including mechanical properties) The kinetics of re-ordering of disordered starting material will be examined,including sluggishly ordering phases (which can be aided by concurrent irradiation). The circumstances under which a partially disordered intermetallic phase may transform into an amorphous form will be outlined.

Common Fixed Point Result of Multivalued and Singlevalued Mappings in Partially Ordered Metric Space

In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.

Separation of Salbutamol by Nano-baskets of Calix[4]arene Bearing Sulfonyl-carboxamides in Partial-cone Conformation

Salbutamol,which increases the muscle mass and decreases the adipose tissue,is misused as nutrient repartitioning agent in the livestock.The novelty of this work is the determination of salbutamol in the livestock meat via new bonded-phases bearing eight derivatives of p-tert-calix[4]arene in partial-cone conformation.The new synthesized bonded-phases were characterized and optimized.The bonding interactions of solute and stationary-phases were examined and the main interactions were reported.The salbutamol levels in six samples of livestock meat were analyzed and the results reveal that for the best bonded-phases,the limit of detection（LOD） and limit of quantitation（LOQ） were 0.02 and 0.06 μg/mL,respectively.

Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.

Feasibility and Structural Feature on Monotone Second-Order Cone Linear Complementarity Problems in Hilbert Space

Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

A New Relationship Between Partial Orders of Normal Matrices and Their Squares

A new relationship between partial orders of normal matrices and their squares is established.

ORDERING CONTRACTION MAPPING PRINCIPLE AND APPLICATIONS

This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.

含SOP的交直流混合配电网日前优化调度

为实现交直流混合配电网的高效运行,提出一种含智能软开关的交直流配电网优化调度方法。在对应用于交直流配电网的智能软开关工作原理进行阐述的基础上,建立含智能软开关的交直流配电网优化调度模型。通过线性化和凸松弛技术,将所建立的非线性优化模型转化为二阶锥规划模型,并且采用改进的50节点算例分析验证模型的有效性。算例结果表明,基于所建模型得到的智能软开关运行策略能够降低配电网运行损耗及改善电压越限的情况,显著提高混合配电网的经济性。

海水淡化厂与区域水-能耦合系统的协同调度

海水淡化厂具有能量密集、运行灵活的特点,是理想的电力需求响应资源。然而,现有关于淡化厂与电网协同运行的研究大多关注电网和淡化厂的一体化调度、无法适应双方自主决策的工程场景,对淡化厂运行约束的刻画也比较粗糙。该文研究反渗透淡化厂与区域水-能耦合系统(waterenergy nexus,WEN)的协同运行方法。首先,考虑淡化厂的生产流程、调节特性和运行约束,分别建立传统及新能源淡化厂的水-能管理模型;其次,在保障两类淡化厂和区域WEN自主决策和信息隐私的条件下,提出以双方调度计划互动为载体的“激励型”和“价格型”两种协同运行机制及调度模型,并提出基于二阶锥松弛和McCormick包络的求解方法。用算例验证所提协同运行机制、调度模型及求解方法的有效性。

基于改进灰狼优化算法的含光伏配电网动态无功优化

针对光伏并网对配电网造成的电压波动、线损增加,以及光伏和负荷出力的不确定性等问题,本文构建基于二阶锥规划的线性凸优化模型,通过控制有载调压变压器和电容器组动作,以及光伏逆变器和静止无功发生器无功补偿能力约束,对日前日内双时间尺度无功优化模型进行动态分析,在简化求解过程的同时加大找到全局最优解的可能性。提出一种基于混沌学习初始化、非线性收敛因子、最优粒子柯西扰动结合蜘蛛猴算法位置更新方式的改进灰狼优化算法,防止算法陷入局部最优并增强其全局搜索能力。最后,运用改进的灰狼优化算法对含光伏的IEEE 33节点系统进行建模仿真,结果表明该算法具有寻优效率高、收敛速度快的优点,验证了算法的可行性和高效性。

偏序半群的商序同态研究

通过偏序半群的商半拟序、商半拟链和正则同余,研究了偏序半群的商序同态,给出了偏序半群的商序同态基本定理。同时,讨论了偏序半群的商半拟序与商序同态之间的关系,给出了由偏序半群S到T的商序同态φ构造S的商半拟序ρ_φ的方法以及S的一个商半拟序ρ?ρ_φ的充分必要条件,并得到了一些重要结论。

属性偏序形式结构的数学形式化

属性偏序形式结构,作为一种基于人类认知原理和粒计算思想的知识发现和知识表示新理论,目前已有广泛的应用,但其理论基础缺乏抽象化数学化,这势必影响该理论的系统发展。针对上述问题,研究了属性偏序形式结构的数学形式化描述问题。首先,基于粒计算的思想提出了知识表示的形式化框架。在此基础上,通过定义对象集合的覆盖和最简覆盖,给出属性偏序形式结构的粒和粒群的概念,进而通过对粒衍生出粒群的充要条件的讨论,给出了属性偏序形式结构中的知识结构,从而完成属性偏序形式结构的数学形式化描述。最后,通过具体实例展示了利用数学形式化描述构造属性偏序形式结构的过程,并揭示了该过程所体现的人类认知规律。

极限下限分析的区域光滑径向点插值法

极限分析的高效数值计算方法在结构设计和安全评定中具有非常重要的作用.为了更加有效地求解极限分析问题,将区域光滑径向点插值法与二阶锥规划相结合,提出了理想弹塑性结构极限下限分析的一种新方法.将问题域离散为简单的三角形背景单元,每个单元进一步划分成若干个光滑域.为了将复杂的域积分转化为简单的边界积分,并且避免计算形函数的导数,采用广义梯度光滑技术对每个光滑域进行应变光滑处理.由于径向点插值法构造的形函数满足Kronecker delta性质,本质边界条件可以直接施加.依据下限定理,在满足以等效积分弱形式表达的自平衡应力场平衡条件的基础上,用二阶锥规划成功构建了极限分析下限法的计算模型,从而可方便地通过基于原始-对偶内点法的数学规划求解器MOSEK直接求解该问题.数值算例结果表明,本文所提方法有效地克服了维数障碍问题,具有较高的计算精度,并且计算结果对网格畸变十分不敏感.

偏序集上非自映射的最佳逼近点定理

给出广义收缩非自映射的概念,证明了该非自映射在偏序集上的最佳逼近点定理,并举例支持本文的研究结果.所得结果推广了相关文献的结论,尤其无偏序关系的距离空间中非自映射的最佳逼近点定理是本文结论的一个特殊情况.

计及电-气双向耦合的综合能源配电网优化重构

综合能源系统是实现电网、气网以及热网等多种能源系统深度融合,利用能量耦合互补等优势提升整个系统能源利用效率的有效形式。为提升综合能源系统优化运行能力,文章首先基于电转气技术与天然气发电技术,构建了的电-气双向耦合综合能源系统总体模型。进而考虑配电网重构技术(Distribution Network Reconfiguration Technology,DNR)中拓扑结构灵活可控这一特性,在配电子系统中引入开关变量、系统运行总费用最低这一目标函数及网络辐射状拓扑结构等约束,建立了配电子系统重构模型。从降低模型求解复杂性的角度,应用二阶锥松弛、乘积变量线性化及分段线性化等方法,将原始综合能源配电网重构非凸非线性模型转化为混合整数二阶锥规划(Mixed Integer Second-Order Cone Programming,MISOCP)问题求解。仿真结果表明,在电-气双向耦合的综合能源系统中应用配电网重构技术,能够降低综合能源系统运行费用,同时有效支撑了配电子系统电压与配气子系统气压。

基于组合赋权-偏序集的应急供应链可靠性评价

为协调好应急供应链中物资的分配与使用,基于文献分析等方法提炼应急供应链可靠性评价指标,建立由组织保障可靠性、系统制度可靠性以及运作流程可靠性3个一级指标及其对应的17个二级指标组成的应急供应链可靠性评价指标体系;利用层次分析法(AHP)、熵权法(EWM)和三角模糊数计算指标权重,将蕴含权重信息的偏序关系引入评价研究中,构建组合赋权-偏序集模型评价应急供应链的可靠性,并应用该模型评价分析C市5个县级城市的应急供应链可靠性水平。结果表明:5个县级城市的应急供应链可靠性程度可分为4类,其中,地区03的可靠性水平高,地区04、02的可靠性水平较高,地区05的可靠性水平中等,而地区01的可靠性水平低;通过对比分析,获取各地区的优势环节和薄弱环节以及需改进的地方。该评价模型可有效评估应急供应链可靠性水平。

考虑电力负荷需求和分布式电源不确定性的配电网重构

随着可再生能源和可变负荷在配电系统中比例的逐步提高,配电网中电力流向的不确定性对最优网络拓扑结构的影响越来越显著。由于分布式发电和需求响应受时间因素影响,按单时段建模所得到的拓扑结构在一天中的不同时段难以达到最优。为解决这种不确定因素的影响,文章提出了一种基于二阶锥优化的配电网重构模型,进行计及需求响应的多时段潮流分析。基于实际配网系统所存在的“源-储-荷”结构,建立了以网络运行成本和开关运行成本为目标的约束条件,利用二阶锥松弛将非凸形式搜索空间转化为凸可行域,从而进行快速求解。在改进的IEEE 33节点配电网上进行测试分析,结果表明,文章提出的方法比传统方法具有更高的准确性和更快的求解速度。