国家天元数学东北中心将于2021年7月2日-7月22日在举办“Control, Machine Learning and Numerics”暑期短课。该课程由Prof. Dr. Enrique Zuazua Friedrich-Alexander University (FAU), Erlangen-Nürnberg (Germany) 开授，旨在为从事该领域研究的青年教师和研究生提供系统性讲解。

一、课程基本信息：

1、授课人：Prof. Dr. Enrique Zuazua

2、授课人单位：Friedrich-Alexander University (FAU), Erlangen-Nürnberg (Germany)

3、课程名称：Control, Machine Learning and Numerics

4、开课时间段：2021年7月2日-7月22日

5、课程学时：36学时

6、课程形式：线上课程

7、预备知识：Optimization, ODE and numerical analysis, machine learning

8、所需教材：

[1] J. M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs, 143, AMS, 2009.

[2] D. Ruiz-Balet and E. Zuazua, Neural ODE control for classification, approximation and transport, arXiv:2014.05278, 2021.

[3] E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods, SIAM Review, 47 (2) (2005), 197-243.

[4] E. Zuazua, Controllability and Observability of Partial Differential Equations: Some results and open problems, in Handbook of Differential Equations: Evolutionary Equations, vol. 3, C. M. Dafermos and E. Feireisl eds., Elsevier Science, 2006, pp. 527-621.

二、课程介绍：

In this series of lectures, we shall first discuss several topics related with the modelling, Analysis, numerical simulation and control of Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) arising in various areas of science and technology.

After a short historical introduction, we shall present and discuss the problem of controllability. It consists in analyzing whether, by means of a suitable and feasible controller, the solution can be driven to a desired final configuration (or close to it).

We shall also discuss its dual version, the so-called observability problem. It concerns the possibility of measuring or observing by suitable sensors, the whole dynamics of the system through partial measurements.

In these lectures we shall try to summarize some of the most fundamental work that has been done in the subject in recent years. we shall also describe and document some of the most relevant applications.

On the other hand, the modern theory of Machine Learning is strongly inspired and influenced by some of the fundamental ideas and techniques in Control Theory. An introduction to this topic will also be presented, focusing mainly on the use of control techniques for the analysis of Deep Neural Networks as a tool to address, for instance, the problem of Supervised Learning.

三、授课人介绍：

Chair in Applied Analysis, Alexander von Humboldt-Professorship. Expert in Applied Mathematics: Partial Differential Equations, Systems Control, Numerical Analysis and Machine Learning.

四、招生及录取：

1、招生对象：从事相关领域研究的青年教师、博士后、博士或高年级硕士生；本次课程为线上课程，不限人数。

2、学员待遇：主办方提供课程资料，学员不需缴纳学费。

3、报名方式：

（1）所有申请参加短课的学员扫描以下二维码或点击链接（https://jinshuju.net/f/qmx6bj），在线提交学员基本信息；将个人证件（工作证，或者学生证）以“姓名+单位+机器学习”的形式命名，扫描或者拍照发送到天元邮箱tianyuanmath@jlu.edu.cn，邮件主题为“姓名+机器学习”。 

（2）此次短课报名截止时间为2021年6月12日，录取结果将于6月18号以后通过网站和邮件的形式通知学员。未入选的不再另行通知。

五、联系方式：

联系人：刘老师

办公电话：0431-85167375

邮箱：tianyuanmath@jlu.edu.cn

地址：吉林大学数学学院315办公室