Mini-symposium (MS) 

MS14:  Numerical Methods and Deep Learning for Nonlinear PDEs

Organizers: Chunmei Wang, University of Florida

                     Sara Pollock, University of Florida

Abstract: Numerical Methods for partial differential equations and their analysis are important and challenging topics in applied and computational mathematics. Deep learning is a method of data analysis that automates analytical model building, which is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns and make decisions with minimal human intervention. This mini-symposium is focused on recent developments in numerical methods and deep learning for PDEs with an focus on nonlinear PDEs, including new developments in finite element methods, deep learning and relevant applications. The goal of this mini-symposium is to bring together leading researchers in the field of numerical methods and deep learning to discuss and disseminate the latest results and envisage future challenges in traditional and new areas of science. The topics of the mini-symposium cover a broad range of numerical methods and deep learning, including but not limited to finite element methods, interior penalty method, extended Galerkin methods, vector-cloud neural networks, weak adversarial networks, etc. A wide range of application fields will also be covered, such as poroelasticity, electroporoelasticity, and phase field crystal equations.

Saturday, September 18, 3:30 PM – 5:30 PM: Part I of II

Room: Libry 4041

3:30 – 4:00 A.J. Meir, Southern Methodist University, On the equations of poroelasticity and electroporoelasticity.

4:00 – 4:30 Xiaojing Ye, Georgia State University, Solving high-dimensional PDEs using weak adversarial networks

4:30 – 5:00 Jiequn Han, Flatron Institute, Learning nonlocal constitutive PDE models with vector-cloud neural networks

5:00 – 5:30 Shijun Zhang, National University of Singapore, Deep network approximation via function composition

Sunday, September 19, 10:30 AM – 12:30 PM: Part II of II

Room: Libry 4041

10:30 – 11:00 Yuehaw Khoo, University of Chicago, Transition path theory with low complexity models

11:00 – 11:30 Traian Iliescu, Virginia Tech, Large eddy simulation reduced order models

11:30 – 12:00 Amanda Diegel, Mississippi State University, A C0 Interior Penalty Method for the Phase Field Crystal Equation

12:00 – 12:30 Yuwen Li, Penn State University, Extended Galerkin methods in finite element exterior calculus