威尼斯人

2019数据科学与优化计算研讨会

会议组织者：张影、岳兴业、杨周旺、康红梅

会务联系人：康红梅（15995703093）

会议地点：南林饭店园中楼一楼涵碧厅

会议时间：2019.11.29-2019.12.01

日程表

学术报告题目与摘要

报告人：金石   上海交通大学

题目：Consensus-based High Dimensional Non-convex Global Optimization in Machine Learning

摘要：We introduce an stochastic interacting particle consensus system for global

optimization of high dimensional non-convex functions. This algorithm does not use gradient of the function thus is suitable for non-smooth functions. We prove that under dimension-independent conditions on the parameters and initial data the algorithms converge to the neighborhood of the global minimum almost surely.

报告人：明平兵 中科院数学与系统科学研究院

题目：A comparison study of some deep learning based numerical method for PDEs

摘要：We shall discuss several deep learning based numerical methods for partial differential equations, the performance of the methods are evaluated. The convergence behavior of the methods will also be studied.

报告人：郭田德 中国科学院大学威尼斯人

题目：组合优化问题的机器学习求解方法

摘要：最优化是人工智能的重要的支撑学科之一，对人工智能的发展起着重要作用。反过来，人工智能又为求解最优化问题提出了新的思路。组合优化问题，特别是大规模的组合优化问题，其快速求解具有重要的理论意义和实际应用价值。为了达到快速求解的目的，一般主要是设计近似算法，这类算法都是基于问题而设计，对于相同问题的不同实例，前面实例的求解经验对后面的实例求解基本没有帮助。围棋人工智能技术的成功表明，深度学习技术可以用来求解一些组合问题，并且在求解实例过程中可以通过逐步积累经验来指导未来实例的求解。本报告首先介绍近年来已经出现的一些利用深度学习求解组合优化问题的开创性工作，然后介绍我们在这方面的最近的一些研究成果，包括利用指向型网络，结合多标签分类的思想，在有监督的训练方式下，求解点集匹配问题，并推广求解德洛内三角剖分等带结构的组合优化问题；针对图匹配问题，我们提出矩阵对称压缩的全局特征提取以及基于双向循环神经网络的局部特征提取方式，结合Actor-Critic强化学习训练方式，在人工数据集以及实际指纹公开库中验证了模型和算法的有效性。

报告人：高卫国 复旦大学

题目：An Alternating SDP Algorithm for Biclustering

摘要：We propose a convex model and an alternating SDP algorithm for bi-clustering which is an extension of the standard clustering. By using some random matrix results, we show that one step iteration achieves the exact solution without noise and still gets very good approximation when noise is presented. Further iterations improve the result in the noise case. The theoretical bound we obtained is better than the existing bounds. Numerical experiments demonstrate the efficiency of our proposed method. This is joint work with Xiuyuan Cheng and Yuxin Ma.

报告人：李铁军   北京大学

题目：Differential network inference via the fused D-trace loss with cross variables

摘要：Detecting the change of biological interaction networks is of great importance in biological and medical research. We proposed a simple loss function, named as CrossFDTL, to identify the network change by estimating the difference between two precision matrices under Gaussian assumption. The CrossFDTL is a natural fusion of the D-trace loss for the considered two networks by imposing the l1 penalty to the differential matrix to ensure sparsity. The key point of our proposal is to utilize the cross variables, which correspond to the sum and difference of two precision matrices instead of using their original form. We developed efficient minimization algorithm for the proposed loss function and rigorously proved its convergence. Numerical results showed that our method outperforms the existing methods in both accuracy and convergence speed for the simulation and real data.

报告人：谢和虎 中国科学院数学与系统科学研究院

题目：非线性方程的多重网格方法

摘要：本报告将介绍求解非线性方程的一种高效有限元多重网格算法。利用多重校正技术把在细有限元空间上非线性问题的求解转化成高维空间上线性方程的求解和在一个低维空间上非线性方程的求解。这样使得我们可以利用高维空间上的高效线性解法器来有效加快非线性方程的求解。这里我们将介绍算法的本质思想以及在非线性问题，特征值问题和非线性特征值问题中的应用。

报告人：戴彧虹 中国科学院数学与系统科学研究院

题目：An Efficient Global Optimization Algorithms for Solving Heated Oil Pipelines Problems

摘要：It is a crucial problem how to heat oil and save running cost for crude oil transport. This paper strictly formulates such a heated oil pipelines problem as a mixed integer nonlinear programming model. Nonconvex and convex continuous relaxations of the model are proposed, which are proved to be equivalent under some suitable conditions. Furthermore, we may provide a preprocessing procedure to guarantee these conditions. Therefore we are able to design a branch-and-bound algorithm for solving the mixed integer nonlinear programming model to global optimality. To make the branch-and-bound algorithm more efficient, an outer approximation method is proposed as well as the technique of warm start is used. The numerical experiments with a real heated oil pipelines problem show that our algorithm achieves a better scheme and can save 6.83% running cost compared with the practical scheme. This is a joint work with Muming Yang, Yakui Huang and Bo Li.

报告人：徐岗 杭州电子科技大学

题目：基于体细分的多分辨率等几何拓扑优化方法

摘要：拓扑优化是创成式设计中的关键技术。但目前的方法通常需要样条拟合、光顺等大量后处理操作才能使拓扑优化结果与CAD系统兼容。此外，实现复杂形状设计、仿真和优化阶段数据表示的无缝集成也是一个具有挑战性的问题。 本报告将介绍一种基于体细分的多分辨率三维等几何拓扑优化框架。 在该框架中，我们采用统一的的三变量样条语言用于几何表示、等几何仿真和拓扑优化，从而得到由光滑样条体表示的最佳拓扑外形，并可直接导入CAD系统。此外，基于体细分的多分辨率性质，可在较低计算成本下实现高质量拓扑优化。给出了基于线弹性问题的若干拓扑优化实例，以展现所提出框架的有效性。

报告人：邓重阳 杭州电子科技大学

题目：An interpolatory view of polynomial least squares approximation

摘要：We derive a formula for weighted polynomial least squares approximation which expresses the approximant as a convex combination of interpolants. There is a similar formula for L2 approximation and the same principle applies to multivariate approximation.

报告人：蔺宏伟 浙江大学

题目：拓扑数据处理及其在时间序列分析方面的应用

摘要：拓扑数据处理以持续同调为主要工具，通过在度量空间中构造一列逐渐“生长”的单纯复形序列，计算持续变化的同调特征（持续同调群中的生成元），并根据这些同调特征的生命周期推断特征的重要程度，从而实现对离散数据点整体拓扑特征的推断和拓扑特征的提取。本报告介绍了持续同调的构造方法、表示形式、稳定性、以及在数据分析、计算机图形学等方面的应用。另外，本报告还介绍了将持续同调与深度学习相结合，在时间序列分析方面的应用。

报告人：申立勇 中国科学院大学

题目：曲面隐式化的新进展

摘要：曲面隐式化问题是计算机辅助（几何）设计，计算机图形学中的一个经典问题，在工程领域有广泛应用。设计高效且鲁棒的有理曲面隐式化方法一个挑战性的问题。目前已有的典型隐式化方法：Groebner基方法，结式方法，动曲面方法，µ基方法，给出它们在理论和效率方面各自的优缺点。结合结式方法，动曲面方法，µ基方法的各自优势，我们提出动曲面结式方法，该首先求得三个代数线性无关的动平面，然后求得并除去动平面结式中的所有多余因子，最后得到隐式方程。新方法复杂度为近似多项式的，适用曲面类型多，因而在理论完备性和计算效率的综合评价上优于当前算法。结合各种方法的优势，我们还开发了Maple曲线、曲面隐式化程序包。传统隐式化都是针对整体曲面的，但是实际应用中，如样条曲面，都是分片表示的，如何给出曲面片的隐式表示进展不多。基于隐式化工作进展，我们通过半代数系统给出了曲面片的一种隐式化表示。

报告人：贾晓红 中国科学院数学与系统科学研究院

题目：椭球碰撞检测理论及应用

摘要：碰撞检测（Collision Detection）是计算机辅助设计和制造、计算机图形学、虚拟现实、数控技术、机器人学、分子动力学模拟等诸多领域的重要问题。我们将以两几何体的三个逐渐深入的几何关系——相对位置、交线形态、交体构型为目标，介绍其逐层深入的代数判定条件，并给出连续碰撞检测的符号算法，以此探索符号计算在碰撞检测及构型分析相关的工业环境中的应用。

报告人：徐大川 北京工业大学

题目：大数据环境下的次模优化

摘要：次模优化广泛研究于计算机,数学,经济学,人工智能等领域. 大数据环境下的次模优化理论及算法设计是研究热点之一. 主要的研究模型包括有: 分布式, 并行, 在线和流模型等. 在流算法中, 数据以流的形式呈现, 其目的是从数据流中抽取满足某些特性的稀疏代表子集;在并行算法中, 通过引入自适应(adaptivity)概念, 来衡量算法迭代轮数深度, 且保证在同一轮迭代中能实现并行计算.我们主要介绍次模最大化问题的流和并行算法, 以及若干拓展问题的流和并行算法的进展.

报告人：张举勇 中国科学技术大学

题目：Anderson Acceleration for Efficient Simulation and Geometry Optimization

摘要：Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for interactive applications. Local-global solvers and ADMM method are usually adopted to solve such problems. However, these solvers suffer from lower convergence rate, and may take a long time to compute an accurate result. In this talk, I will introduce our recent work on how to use anderson acceleration to speed up the convergences of these algorithms.

报告人：陈景润 苏州大学

题目：Quasi-Monte Carlo sampling: A better way to overcome the curse of dimensionality for machine-learning PDEs

摘要：Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. Sampling strategy, such as Monte Carlo method, is used to overcome the curse of dimensionality. In this presentation, we use two examples to demonstrate how quasi-Monte Carlo sampling from classical numerical analysis provides a better compromise between accuracy and efficiency. The first example is the estimation of exciton diffusion length (EDL), which plays a vital role in the function of many organic semiconducting opto-electronic devices. The dependence of EDL on surface roughness poses a challenging problem because the parameterization of heterojunctions in high-dimensional random space is far beyond the capability of classical simulation tools. We develop a novel method based on deep neural network to extract a function for exciton diffusion length on surface roughness with high accuracy and unprecedented efficiency, yielding an abundance of information over the entire parameter space. The second example the replacement of of Monte-Carlo method by quasi-Monte Carlo sampling to approximate the loss function. To demonstrate the idea, we conduct numerical experiments in the framework of deep Ritz method proposed by Weinan E and Bing Yu. For the same accuracy requirement, it is observed that quasi-Monte Carlo sampling reduces the size of training data set by more than two orders of magnitude compared to that of MC method. Under some assumptions, we prove that quasi-Monte Carlo sampling together with the deep neural network generates a convergent series with rate proportional to the approximation accuracy of quasi-Monte Carlo method for numerical integration. Numerically the fitted convergence rate is a bit smaller, but the proposed approach always outperforms Monte Carlo method. It is worth mentioning that the convergence analysis is generic whenever a loss function is approximated by the quasi-Monte Carlo method, although observations here are based on deep Ritz method.

报告人：杨周旺 中国科学技术大学

题目：Theoretical investigation of generalization bound for residual networks

摘要：This paper presents a framework for norm-based capacity control with respect to a weight-normalized residual neural networks (ResNets). We first formulate the representation of each residual block. For the regression problem, we analyze the Rademacher complexity of the ResNets family and establish a tighter generalization upper bound for weight-normalized ResNets. Using the (p, q)-norm weight normalization in which 1/p+1/q>=1, we discuss the properties of a width independent capacity control, which only relies on the depth according to a square root term. Several comparisons suggest that our result is tighter than previous work. Parallel results for deep neural networks (DNN) and convolutional neural networks (CNN) are included by introducing the (p,q)-norm weight normalization for DNN and the (p,q)-norm kernel normalization for CNN. Numerical experiments also verify that ResNet structures contribute to better generalization properties.