Data-Driven Modeling and Learning Using the Weak Form
BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations
报告人 David Bortz University of Colorado Boulder
时 间 08:50-12:15 Thu
地 点 1129B Zoom 537 192 5549（PW: BIMSA）
Data-driven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will discuss several ubiquitous challenges with the conventional model development / discretization / parameter inference / model revision loop (illustrating the issues with examples from Microbial Electrolysis Cells, chemotaxis, and HIV viral dynamics). I will present our Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) framework which addresses several of these challenges and offers substantial advantages in terms of computational efficiency, noise robustness, and modest data needs (in an online learning context). Lastly, I will illustrate applications of WSINDy to several benchmark problems as well as to the inference of interacting particle systems, specifically learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population.
Prof. Bortz earned his PhD in 2002 with H.T. Banks at North Carolina State University. He was then a postdoc at the University of Michigan in Mathematics and joined the faculty in Applied Math at the University of Colorado in 2006. The core of his research interests are in scientific computation methodologies for data-driven modeling and inverse problems at the intersection of applied math and statistics. His research has received support from NSF, NIH, DOE, DOD, and NVIDIA.
组织者：熊繁升, 杨武岳, 雍稳安, 朱毅
Topological correlators of 4d N=2* and 5d N=1 super Yang-Mills
Geometry and Physics Seminar
报告人 Jan Manschot Trinity College Dublin
时 间 10:00-11:00 Thu
地 点 1131 Zoom 293 812 9202（PW: BIMSA）
组织者：Hossein Yavartanoo, 张其明
Path Integral and Casimir Force for Higher Derivative Actions
BIMSA General Lecture
报告人 Bing Miao UCAS, Lanzhou University
时 间 10:45-11:45 Thu
地 点 1108 Zoom 559 700 6085（PW: BIMSA）
Since its introduction into physics through the discussion of vacuum zero point quantum fluctuation, the Casimir force has been generalized to cover a wide spectrum of topics related to fluctuations whose origins could be quantum/thermal, equilibrium/non-equilibrium. In this talk, I will start with a short survey on the history of Casimir physics, then discuss our recent work where, based on a method developed by us to exactly calculate the Feynman path integrals involving higher derivative actions, we generalized the critical Casimir force in the Landau-Ginzburg-Wilson theory to the Brazovskii-type field theories with zero modes of finite wavelengths.
Bing Miao is a Professor at the University of Chinese Academy of Sciences and an Adjunct Professor at the Lanzhou University. He obtained his PhD in theoretical polymer physics from the Chinese Academy of Sciences in 2006. Then he was a postdoc in Physics Department of St. Francis Xavier University and University of Guelph in Canada (2006. 5-2008. 9), and Theory Department of Max Planck Institute for Polymer Research in Germany (2008. 10-2011. 2). He joined UCAS since 2011. He has a wide interest in fluctuation-related physics and mathematics.
Geometry and topology in collective dynamics models
Tsinghua-BIMSA Applied and Computational Math Colloquium
报告人 Pierre Degond Institut de Mathématiques de Toulouse CNRS, Université Paul Sabatier
时 间 15:30-16:30 Thu
地 点 Zoom 276 366 7254（PW: YMSC）
Collective dynamics arises in systems of self-propelled particles and plays an important role in life sciences, from collectively migrating cells in an embryo to flocking birds or schooling fish. It has stimulated intense mathematical research in the last decade. Many different models have been proposed but most of them rely on point particles. In practice, particles often have more complex geometrical structures. Here, we will consider particles as rigid bodies whose body attitude is described by an orthonormal frame. Particles tend to align their frame with those of their neighbours. A hydrodynamic model will be derived when the number of particles is large. It will be used to exhibit solutions having non-trivial topology. We will investigate whether topology provides enhanced stability against perturbations, as observed in other systems such as topological insulators. This talk is based on recent results issued from collaborations with Antoine Diez, Amic Frouvelle, Sara Merino-Aceituno, Mingye Na and Ariane Trescases.
Prof. Degond was trained at the Ecole Normale Supérieure in Paris and his first appointment was in Ecole Polytechnique in Palaiseau in 1985 as a Junior Researcher at CNRS. He was then appointed a full Professor in Ecole Normale Superieure of Cachan in 1990. He joined back the CNRS in Toulouse as a Senior Researcher in 1993, where he founded the Applied Math group, and holds a permanent position. He has been a Chair Professor in Applied Mathematics at Imperial College in the period 2013-2020, and a Visiting Professor in Mathematics afterwards. He is interested in plasma physics, rarefied gas dynamics, semiconductor modeling, collective dynamics, decision making and self-organization in complex systems arising from biology and social sciences. His methods combine analysis, asymptotic theory and multiscale numerical techniques. He has been been an invited speaker at the 2018 International Congress of Mathematicians (ICM 2018). He was awarded the Jacques-Louis Lions prize 2013 of the French Academy of Sciences and a Royal Society Wolfson Research Merit Award holder in 2014-2018.