时间：7月9号上午9:30-10:30

地点：学院三楼会议室

报告人：苏州大学 康红梅博士

主题：An Economical Representation of PDE Solution by  using Compressive Sensing Approach

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个人简介：

康红梅，苏州大学数学学院副教授。2009 从吉林大学数学学院毕业，同年保送至中国科学技术大学数学学院计算数学方向攻读博士，导师为陈发来教授。2016  年3月至  2017 年3月在意大利国家研究所 CNR-IMATI从事博士后研究，合作导师为Annalisa Buffa。主要研究领域为计算机辅助几何设计 (CAGD)、几何建模、样条函数逼近、图像处理等。近年来开始关注机器学习，主要研究兴趣是借助于深度学习技术解决传统CAGD和几何建模中的问题。

Abstract：

We  introduce a redundant basis for numerical solution to the Poisson equation and  find a sparse solution to the PDE by using a compressive  sensing approach. That is, we refine a partition of the underlying domain of the  PDE several times and use the multi-level nested  spline subspaces over these refinements to express the solution of the PDE  redundantly. We then use a compressive sensing algorithm  to find an economical representation of the spline approximation of the PDE  solution. The number of nonzero coefficients of  an economical representation is less than the number of the standard spline  representation over the last refined partition, i.e. finite

element  solution while we will show that the error of the spline approximation with an  economical representation is the same to the standard  FEM solution. This approach will be useful, e.g. in the situation when the PDE  solver has a much powerful computer than the  users of the solution