# Workshop on Mathematical Machine Learning and Application

The Workshop on Mathematical Machine Learning and Application will take place on April 27-29, 2020. Workshop will be held in room 114 of the Department of Mathematics of Penn State, located at McAllister Building, Pollock Rd, State College, PA.
There is also a short course “A Mathematical Introduction to Deep Learning” which will be given by Jinchao Xu from Penn State in the afternoon at 2:00pm-5:00pm Sunday, April 26 2020.

## Overview

Today, machine learning is a hot topic with important practical applications. Notable successes are the classification problems for identifying pictures and the Artificial Intelligence (AI) Go-player, AlphaGo Zero, which beat the best human player in the world. While these successes indicate that we are making progress toward applying AI to various important tasks, there are many emerging scientific questions. For instance, how can we understand these empirical successes in a mathematically rigorous way, using approximation theory and probability theory? Can we develop a theory which can guarantee the success of machine learning models in certain situations? How can we apply ideas from machine learning to existing problems in numerical analysis, such as Bayesian inference, operator estimation, solving PDE’s, density estimation, sampling methodology, and uncertainty quantification. Can machine learning be applied to the mathematical modeling of dynamical systems that historically relies on first principle calculations?

This workshop aims to bring together leading experts across scientific disciplines to discuss recent efforts in addressing these questions. Our hope is that the activity will inspire and attract participants to work on related mathematical problems in this emerging field and hopefully contribute to the development of the modern data-driven scientific computational methods to address these questions.

## Schedule

• Short Course ( Sunday, April 26 2020).
Time Speaker Title and Abstract
2:00-5:00pm Jinchao Xu, Penn State University
• Title: A Mathematical Introduction to Deep Learning
• Abstract: This 3-hour short course is devoted to an elementary and self-contained introduction to deep learning from a mathematical viewpoint.  Models and algorithms from two different subject fields will be presented: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods.  Mathematical relationships between these models and algorithms will be explored and used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular,  a new convolutional neural network (CNN), known as MgNet,  will be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then discuss the theoretical and practical potentials of MgNet.   If time allows, approximation properties of deep neural network functions and convergence analysis of stochastic gradient descent methods will also be presented.

## Registration/Logging

Please fill the form for registration here.

Please note due to limited capacity, the deadline to register for the workshop is March 26th.

If funding is available and you would like to apply for support, please email Natasha Urbanik at nzu10@psu.edu the following:

• Cover Letter
• CV
• Statement about research & motivation to participate in the workshop
• Estimated support requested
**Please continue to check back for funding updates as they become available**

Lodging reservations for the Invited Speakers will be made by the Department.

Participants can stay at the Days Inn or Hyatt Place State College. Participants should make their own hotel reservations and guarantee with a valid credit card. Guests will pay for their own lodging at the hotel during checkout. Please call hotel phone number listed, code will not work with the online system.

Days Inn: 1-800-258-3297 or 814-238-8454. Reference group code 042620PSU. Rates are $94+tax(two beds)/night. Reservations with PSU discount must be made on or before March 26, 2020. Hyatt Place State College: 1-888-492-8847. Reference group code . Rates are$109+tax(two beds)/night. Reservations with PSU discount must be made on or before April 3, 2020.

Should you decide change your arrival/departure dates or if you should decide not to attend, please contact the hotel directly. Please note: cancellation fees, early depature fees and no-show policies effective.

## Organizing Committee

Jinchao Xu (The Pennsylvania State University)

John Harlim (The Pennsylvania State University)

Juncai He (The Pennsylvania State University)

Jonathan Siegel (The Pennsylvania State University)

## Workshop Staff Assistant

Natasha Urbanik: nzu10@psu.edu