• University of South Carolina
  • Smart State SC

Spring School Series

2019: Models and Data

March 17, 2019 – March 20, 2019

University of South Carolina

Sumwalt College

Columbia, SC 29208

Sponsored by the National Science Foundation

About the Conference

This is the second Spring School being hosted by the DASIV SmartState Center. This year, we have been funded by the National Science Foundation to support all participants. In our inaugural year, 2018, we hosted a very eager group of young researchers and postdocs from Southern California to Massachusetts. Based on the success of last year’s conference, we will follow the same format this year. We will feature six lecturers who are considered high-caliber representatives of their respective area of expertise. The lectures are to be tutorial in nature, interactive, and will be interlaced with open, group discussions. We are anxious for all participants to engage in active collaboration.

The interactive lectures are going to cover a diversity of topics organized under our main theme, namely to foster synergetic syntheses of on the one hand classical “model-based” and, on the other hand “data-driven” methodologies. The topics addressed in the Spring Schools pertain to ongoing vibrant developments in areas like machine learning, notable deep learning, computation harmonic analysis, as a pillar in data science, or Uncertainty Quantification and related modeling or numerical analysis aspects.

The Spring Schools attempt to contribute forming a corresponding mindset at a possibly early stage of a scientific career. We believe that the very topics addressed in the planned workshop series and their interrelation represent important developments in many areas of applied and theoretical sciences. The Spring Schools will foster the necessary critical thinking of young researchers, encourage their openness to perhaps unconventional approaches.

We invite postdocs, graduate students, and young researchers to participate in this event. If you would like to attend this Spring School, apply to be a participant by March 6, 2019.

Organizing Committee

List of Speakers

Albert CohenSlides Talk

Least-Squares Methods for High Dimensional Problems

Various mathematical problems are challenged by the fact they involve functions of a very large number of variables. Such problems arise naturally in learning theory, partial differential equations or numerical models depending on parametric or stochastic variables. They typically result in numerical difficulties due to the so-called "curse of dimensionality". We shall first discuss how these difficulties may be theoretically handled in the context of stochastic-parametric PDE’s through the concept of sparse polynomial approximation. We shall then focus on a class of concrete algorithms based on least-squares fitting that provably achieve the convergence properties of these approximations.

Ronald A. DeVoreSlides Talk

An Overview of Approximation of Functions of Many Variables

We discuss Approximation in High Dimensions, focusing on entropy widths, optimal recovery, model classes, etc. We will round out the discussion with polynomial approximation in high dimensions and neural networks, which is only peripherally high dimensional.

Gitta KutyniokSlides 1 Slides 2 Talk

Theory of Deep Learning

Dr. Kutyniok’s main research topics include applied harmonic analysis, compressed sensing, data science, deep learning, frame theory, high dimensional data analysis, imaging science, inverse problems, machine learning, numerical analysis of partial differential equations, sparse approximation.

Eitan TadmorTalk

Collective dynamics: emergent behavior with long-range and short-range interactions

Collective dynamics is driven by alignment that tend to self-organize the crowd, and by different external forces that keep the crowd together. Prototype models based on environmental averaging are found in opinion dynamics of human networks, self-organization of biological organisms, and rendezvous of mobile systems. Different emerging equilibria are self-organized into parties, flocks, tissues, etc.

I will overview recent results of collective dynamics driven by different "rules of engagement". I begin with a survey of several classical models of agent-based systems, and follow with two fundamental questions that arise in the context of such systems, namely --- their large time behavior and their large crowd dynamics. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions. I conclude with a general framework which describes the competition between pairwise alignment with external forcing.

Changhui TanSlides Talk

Asymptotic Preserving Schemes on Kinetic Models with Singular Limits

We will discuss kinetic models with singular hydrodynamic limits. The asymptotic preserving (AP) schemes aim to provide a universal solver for both the full system and the limit system, in the sense that the stability does not depend on the parameter. For systems that have mono-kinetic singular limits, standard AP schemes lose accuracy when the parameter is close to the limit. To overcome such difficulty, we introduce a velocity scaling method that transforms the singular limit to a non-singular one, and build AP schemes on the transformed systems.

Agenda and Schedule of Events

 
8:00 am
8:30 am
9:00 am
9:30 am
10:00 am
10:30 am
11:00 am
11:30 am
12:00 pm
12:30 pm
1:00 pm
1:30 pm
2:00 pm
2:30 pm
3:00 pm
3:30 pm
4:00 pm
4:30 pm
5:00 pm
5:30 pm
6:00 pm
6:30 pm
7:00 pm
Sunday Sun Mar 17
 
Welcome / Opening

Dr. Ronald DeVore

An Overview of Approximation of Functions of Many VariablesAn Overview...

Sumwalt 219 • Slides Talk

Break

Meet & Greet

All Participants

Welcome Reception

Hosted by DASIV

Monday Mon Mar 18

Continental Breakfast

Coffee

Dr. Eitan Tadmor

Collective Dynamics: Emergent Behavior with Long-Range and Short-Range InteractionsCollective Dynamics...

Sumwalt 219 • Talk

Break

Dr. Changhui Tan

Asymptotic Preserving Schemes on Kinetic Models with Singular LimitsAsymptotic Preserving...

Sumwalt 219 • Slides Talk

Lunch

Hosted by DASIV

Dr. Albert Cohen

Least-Squares Methods for High Dimensional ProblemsLeast-Squares Methods...

Sumwalt 219 • Slides Talk

Break

Qingguang Guan

Poor Global Optima for Fully Connected Deep ReLU Neural Networks - Special Examples for HD ApproximationPoor Global Optima...

Sumwalt 219 • Slides Talk

Adjourn
Tuesday Tue Mar 19

Continental Breakfast

Coffee

Dr. Albert Cohen

Least-Squares Methods for High Dimensional ProblemsLeast-Squares Methods...

Sumwalt 219 • Slides Talk

Break

Dr. Eitan Tadmor

Collective Dynamics: Emergent Behavior with Long-Range and Short-Range InteractionsCollective Dynamics...

Sumwalt 219 • Talk

Lunch

Hosted by DASIV

Dr. Gitta Kutyniok

Theory of Deep Learning

Sumwalt 219 • Slides 1Talk

Break

Breakout Discussion

Adjourn
Wednesday Wed Mar 20

Continental Breakfast

Coffee

Dr. Gitta Kutyniok

Theory of Deep Learning

Sumwalt 219 • Slides 2Talk

Break

Short Presentations

Majid Noroozi• Talk

Simon Brugiapaglia • Slides Talk

Victor DiCaria • Slides Talk

Lunch

Hosted by DASIV

CLOSING

Parking

The workshops will take place in Sumwalt Building. The closest parking area with hourly rates is located at the Bull Street Garage.

Visitor Parking Options

University of South Carolina Parking and Transportation Services

1501 Pendleton Street

Columbia, SC 29208

Phone: 803.777.5160

Email: parking@mailbox.sc.edu

Hours of Operation: 8 a.m. – 5 p.m.

University of South Carolina Parking and Shuttle Map

Contact and Map

Coreen Williams, Office Manager

Office: LeConte 317G

Phone: 803.576.6795

eMail: will4457@mailbox.sc.edu

Workshop Location: Sumwalt Room 102

Campus Map

Apply to be a Participant

The DASIV SmartState Center invites all Math Graduate students to consider applying to attend the 2019 Spring School at the University of South Carolina. There is no participation fee to attend however seats are very limited.

Application Deadline: February 20, 2019

You will be responsible for your own travel and accommodations. Please inquire via email to DASIV@math.sc.edu if you might require assistance with travel accommodations. The DASIV Center may have some funds available to assist you.

We are interested in you and your work. Please review the following information BEFORE starting your application. A completed application packet will include the following:

  • Event Registration (Requires a Google accout)
  • Short National Science Foundation Style Biography. (See this example )
  • One-page description of your research interest
  • Evaluator Form – This form should be filled out by a faculty member that you have worked with. It must be submitted by the evaluator via his or her work or personal email. Instructions are on the form.