AM Seminar: Structure-Preserving Discretizations and their Applications
Presenter: Andy Wan, Assistant Professor, University of California, Merced
Description: Many models from science and engineering possess fundamental structures which are important to preserve in order for accurate and stable long-term predictions. For instance, preserving conserved quantities, such as energy, mass and momentum, are fundamental in many physical systems. Moreover, preserving dissipative quantities, such as entropy or Lyapunov functions, are also essential for predicting correct asymptotic limits. In this talk, we will survey a recent new class of conservative and dissipation-preserving integrators, called the Discrete Multiplier Method (DMM). We will discuss various applications to many-body systems, geodesic flow, and particle methods in fluids and kinetic models. Moreover, we will introduce Conservative Hamiltonian Monte Carlo, which utilizes DMM to improve sampling efficacy of Hamiltonian Monte Carlo for high dimensional target distributions. If time permits, we will also discuss how structure-preservation in scientific machine learning can improve long-term predictions and be amenable to error analysis on accuracy bounds.
Bio: Andy Wan is an Assistant Professor in the Department of Applied Mathematics at the University of California, Merced (UC Merced). Prior to joining UC Merced in 2024, he received his Ph.D. from Polytechnique Montreal, and was a postdoctoral fellow at McGill University and later an assistant professor at the University of Northern British Columbia. His research interests are in numerical analysis, scientific computing, and scientific machine learning. He focuses on structure-preserving discretizations, specifically in the theory and development of conservative and dissipation-preserving integrators, as well as their applications to mathematical sciences, computational statistics and scientific machine learning. He is currently a co-investigator of the 2024-2027 Collaborative Research Group on “Structure-Preserving Discretizations and their Applications”, supported by the Pacific Institute for the Mathematical Sciences (PIMS). He has also recently co-organized a summer school and hackathon event on “Structure-Preserving Scientific Computing and Machine Learning”, supported by NSF and PIMS.
Hosted by: Professor Julie Simons
