Events

Department of Mathematics, SMU

Room: 126 Clements Hall (Refreshment starts 15 minutes before talks)

**[1] Thursday, 2/7/2019**

Speaker: Guofei Pang, Applied Math, Brown, 3:45-4:45p, Thursday, 2/7/2019

Title: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems of PDEs and fractional PDEs

Dr. Guofei Pang, Division of Applied Mathematics, Brown University

Abstract: Other than industrial applications such as image recognition and speech analysis, deep learning can solve PDEs as well! In this talk, the speaker will first review the recent progress on applying deep learning to PDE solution, and then introduce the physics-informed neural networks (PINNs) that are able to solve the forward problem and parameter identification problem of PDEs. Thanks to the auto-differentiation routine in the Google’s TensorFlow, one can minimize automatically the discrepancy between the neural network approximation version of governing equation and initial-boundary conditions and the original version. Finally, the speaker will demonstrate his recent work of extending PINNs to fractional PINNs that can solve differential equations involving integral and/or integro-differential terms.

References:

[1]. Raissi, M., P. Perdikaris, and G. E. Karniadakis. "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Journal of Computational Physics 378 (2019): 686-707.

[2]. Pang, Guofei, Lu Lu, and George Em Karniadakis. "fPINNs: Fractional physics-informed neural networks." arXiv preprint arXiv:1811.08967 (2018).

Biosketch:

Guofei Pang is currently a postdoc in Prof. George Karniadakis’s group at division of applied mathematics, Brown University. He received his B.A. in applied mathematics in 2010 and Ph.D. in engineering mechanics in 2015 at Hohai University, China. His current research focus is statistical learning for solving PDEs as well as fractional derivative equations. He published 19 journal papers and one book chapter.

**[2] Thursday, 2/28/2019**

Speaker: Eitan Tadmor, Math, University of Maryland, 3:45-4:45p, Thursday, 2/28/2019

Title: Emergent behavior in collective dynamics

Dr. Eitan Tadmor, University of Maryland

ABSTRACT: Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different “rules of engagement”. 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.

Bio-sketch: Eitan Tadmor is a Distinguished University Professor at the University of Maryland, College Park (UMd). After gaining his Ph.D. from Tel Aviv University in 1979, and a post-doc as a Bateman Instructor in CalTech, 1980-1982, he returned to his alma mater in 1983, where he later chaired the Department of Applied Math, 1991-1993. In 1995 Tadmor joined the UCLA Math Department where he was the founding co-director of the NSF Institute for Pure and Applied Math (IPAM), 1999-2001. In 2002, he was recruited to lead the UMd Center for Scientific Computation and Math Modeling (CSCAMM), and served as its first Director during the fourteen-year period of 2002-2016. Tadmor holds joint appointment in CSCAMM, the Math Department and IPST.

Tadmor delivered an invited lecture at the ICM2002 (Beijing), plenary addresses in the international conferences on hyperbolic problems (Zurich 1990 and Beijing 1998), the SIAM invited address at the 2014 Joint Math Meeting and the 2016 Leçons Jacques-Louis Lions at the Université Pierre et Marie Curie. In 2012 he was in the inaugural class of AMS Fellows. He was the Principal Investigator (PI) for NSF Focus Research Group on “Kinetic Description of Multiscale Phenomena'' (2008-2012), and the NSF Research Network “Kinetic Description of Emerging Challenges in Natural Sciences'' (Ki-Net, 2012-2019). In 2015, he was awarded the SIAM-ETH Henrici prize for “original, broad and fundamental contributions to the applied and numerical analysis of nonlinear differential equations''. In 2016-2017 he was a Senior Fellow at the Institute for Theoretical Studies at ETH-Zürich.

**[3] Tuesday, 3/5/2019**

Speaker: Bo Li, Math, UCSD, 3:45-4:45p, Tuesday, 3/5/2019

Title: Predict the Ligand-Receptor Binding/Unbinding Kinetics with the Variational Implicit-Solvent Model and the String Method

Dr. Bo Li

Department of Mathematics and Quantitative Biology Graduate Program

University of California, San Diego

Abstract: The ligand-receptor binding/unbinding is a complex biophysical process in which water plays a critical role. To understand the fundamental mechanisms of such a process, we have developed a new and efficient approach that combines our level-set variational implicit-solvent model with the string method for transition paths, and have studied the pathways of dry-wet transition in a model ligand-receptor system. We carry out Brownian dynamics simulations as well as Fokker-Planck equation modeling with our efficiently calculated potentials of mean force to capture the effect of solvent fluctuations to the binding and unbinding processes. Without the description of individual water molecules, we have been able to predict the binding and unbinding kinetics quantitatively in comparison with the explicit-water molecular dynamics simulations. Our work indicates that the binding/unbinding can be controlled by a few key parameters, and provides a tool of efficiently predicting molecular recognition with application in drug design.

Biosketch: Bo Li received a Ph.D. in mathematics and an M.S. in mechanics both from the University of Minnesota in 1996. He was a postdoc at the University of California, Los Angeles, from 1996 to 1999, and an assistant professor at the University of Maryland, College Park, from 1999 to 2004. He was an associate professor of mathematics from 2004 to 2010, and has been a full professor of mathematics since 2010, at the University of California, San Diego. Bo Li's research areas include scientific computing and numerical analysis, and applied aspects of partial differential equations, dynamical systems, and stochastic process, with applications to continuum mechanics and material science, and more recently biological physics and computational biology. His research has been supported by the NSF, NIH, and DoE.

**[4] Wednesday, 3/20/2019**

Speaker: Greg Gbur, Physics UNC Charlotte, 3:30-4:30p, Wednesday, 3/20/2019

Title: Infinite Hotels in Swirling Beams of Light

Abstract: Is it possible to see the mathematics of infinite sets play out in a physical system? It has recently been demonstrated, in a number of ways, how optical systems possessing wavefield singularities -- optical vortices and related objects -- can manifest, or even rely on, infinite arithmetic. In particular, several systems have been shown to act out a classic thought-experiment known as Hilbert's Hotel, in which an infinite hotel can be shown to be simultaneously completely occupied and have infinite vacancies. The physics of optical vortices, and their connection to Hilbert's Hotel, are discussed in this talk.

Biosketch: Greg Gbur is a theoretical physicist specializing in classical optics, in particular optical vortices, statistical optics, and invisibility. He currently has over 90 peer-reviewed publications, including three review articles in the long-running series Progress in Optics and four papers in the top physics journal Physical Review Letters. Professor Gbur’s first book, Mathematical Methods for Optical Physics and Engineering, was published in 2011 by Cambridge University Press; his second book, Singular Optics, was published in November 2016 by CRC Press. His third book, a popular science and history book titled Falling Felines and Fundamental Physics, will be released in mid-2019. He is a Senior Member of the Optical Society of America and a topical editor for the Journal of the Optical Society of America A.

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**[5] Thursday, 3/28/2019**

Speaker: Karen Wilcox, Professor and Director of the Oden Institute, University of Texas Austin, Thursday, 3:45-4:45p, 3/28/2019

Title: Projection-based Model Reduction: Formulations for Scientific Machine Learning

Abstract: The field of model reduction encompasses a broad range of methods that seek efficient low-dimensional representations of an underlying high-fidelity model. A large class of model reduction methods are projection-based; that is, they derive the low-dimensional approximation by projection of the original large-scale model onto a low-dimensional subspace. Model reduction has clear connections to machine learning. The difference in fields is perhaps largely one of history and perspective: model reduction methods have grown from the scientific computing community, with a focus on reducing high-dimensional models that arise from physics-based modeling, whereas machine learning has grown from the computer science community, with a focus on creating low-dimensional models from black-box data streams. This talk will describe an approach that blends the two perspectives and provide advances towards achieving the goals of Scientific Machine Learning. We combine lifting--the introduction of auxiliary variables to transform a general nonlinear model to a model with polynomial nonlinearities--with proper orthogonal decomposition (POD) and operator inference. The result is a data-driven formulation to learn the low-dimensional model directly from data, but a key aspect of the approach is that the lifted state-space in which the learning is achieved is derived using the problem physics. Case studies demonstrate the importance of embedding physical constraints within learned models, and also highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models.

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**[6] Thursday, 4/4/2019**

Speaker: Shiwei Zhang, Physics W&M, Flatiron Institute, 3:45-4:45p, Thursday, 4/4/2019

Title: Ab initio computations in quantum many-body systems

Abstract: Accurate and predictive computations of interacting quantum many-body systems represent one of the great challenges in modern physical and computational sciences. I will give an introduction to the problem, which involves solving partial differential equations in high dimensions for solutions that obey global (anti-)symmetry from the exchange of fermions (such as electrons). I will discuss our recent efforts to address the problem using stochastic processes, and comment on some of the mathematical challenges.

Bio-sketch: Shiwei Zhang is a Senior Research Scientist/Group Leader at the Center for Computational Quantum Physics. He is also Chancellor Professor of Physics at the College of William & Mary. Shiwei received his Ph.D. in Physics from Cornell University in 1993. After two years at Los Alamos National Laboratory as a Postdoctoral Research Associate and then a year at Ohio State University as an NSF CISE Postdoctoral Fellow and University Postdoctoral Fellow, he joined the William & Mary faculty in 1996. Shiwei has held visiting positions at many institutions including the University of Illinois, SISSA at Trieste, the Chinese Academy of Sciences. Shiwei has received a number of awards, including the NSF CAREER Award, the Cottrell Scholar Award, and the William and Mary Plumeri Award for Faculty Excellence and is a Fellow of the American Physical Society.

**[7] Wednesday, April 10, 2019 **

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Speaker: Dr. Elton P. Hsu, Department of Mathematics, Northwestern Universit, 3:15-4:45p, Wednesday, 4/10/2019

Title: Brownian motion, History, Theory, and Applications

Abstract: We will briefly review the historical development of Brownian motion from Brown and Einstein to Wiener and Ito. We then discuss some major theoretical results in stochastic analysis of Brownian motion, such as stochastic integration and stochastic differential equations. The wide ranging application of Brownian motion is explained through its use in partial differential equations, differential geometry, financial mathematics, and numerical analysis.

Biographical Sketch: Professor Hsu obtained his Ph. D. from Stanford University and held academic positions at New York University, University of Illinois at Chicago, and University of Minnesota before joining Mathematics Department of Northwestern University. His main area of research is stochastic analysis and its applications to analysis, including partial differential equations, differential geometry, and infinite dimensional analysis. He is the author of a popular graduate textbook on stochastic analysis on manifolds.

**[8] Thursday, 4/18/2019**

Speaker: Longfei Li, Math, LSU, Thursday, 3:45-4:45p, 4/18/2019

Title: A stable partitioned FSI algorithm for incompressible flow and deforming beams

Abstract: A new partitioned algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic structures undergoing finite deformations. The new algorithm, referred to as the Added-Mass Partitioned (AMP) scheme, overcomes the added-mass instability that has for decades plagued partitioned FSI simulations of incompressible flows coupled to light structures. Within a Finite-Difference framework, the AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The stability and accuracy of the AMP scheme is validated through mode analysis and numerical experiments. Aiming to extend the AMP scheme to an Finite-Element framework, we also develop an accurate and efficient Finite-Element Method for solving the Incompressible Navier-Stokes Equations with high-order accuracy up-to the boundary.

Biosketch: Dr. Longfei Li earned his B.S. in Mathematics from Sichuan University in 2009, and received his M.S. and Ph.D. in Applied Mathematics from the University of Delaware under the supervision of Professor Richard Braun in 2011 and 2014, respectively. Dr. Li was subsequently appointed the Margaret A. Darrin Postdoctoral Fellow at Rensselaer Polytechnic Institute (RPI) working with Professor Henshaw, before joining the faculty in the Department of Mathematics at the University of Louisiana at Lafayette as an assistant professor in August, 2017. Dr. Li's research interests broadly lie in the development, analysis and implementation of high-performance computational algorithms to solve partial differential equations (PDEs) and the formulation of mathematical models for multi-physics problems.

**[9] Thursday, 5/2/2019**

Speaker: Jianfeng Lu, Math, Duke, Thursday, 3:45-4:45p, 5/2/2019

Title: Solving large-scale leading eigenvalue problem

Abstract: The leading eigenvalue problems arise in many applications. When the dimension of the matrix is super huge, such as for applications in quantum many-body problems, conventional algorithms become impractical due to computational and memory complexity.In this talk, we will describe some recent works on new algorithms for the leading eigenvalue problems based on randomized and coordinate-wise methods (joint work with Yingzhou Li and Zhe Wang).

Biosketch: Jianfeng Lu is currently an Associate Professor of Mathematics, Physics, and Chemistry at Duke University. Before joining Duke University, he obtained his PhD in Applied Mathematics from Princeton University in 2009 and was a Courant Instructor at New York University from 2009 to 2012. He works in mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, and materials science. His work has been recognized by a Sloan Fellowship, a NSF Career Award, and the 2017 IMA Prize in Mathematics and its Applications.