报告人：彭志超

报告题目：Reduced order model for kinetic and transport problems

报告摘要：Reduced order model (ROM) is a technique to reduce degrees of freedom needed in numerical simulations. In this talk, I will share our recent work on the ROMs for kinetic and transport equation.

In the first part of this talk, we will discuss a ROM for the radiative transfer equation (RTE) based on the micro-macro decomposition. RTE is a kinetic equation which models particle systems in nuclear engineering and astrophysics. One of the main challenges to numerically solve this equation is due to its high dimensional nature, and standard grid-based method may suffer from the curse of dimensionality. To mitigate the curse of dimensionality, we construct a ROM by projecting the original problem to some low dimensional surrogate space.

In the second part, we will discuss a ROM for transport problems. Due to the slow decay of Kolmogorov n-width for some transport problems, classical linear ROMs may be inefficient or even inaccurate for these problems. The underlying low rank structure of these problems may be more efficiently captured through some intrinsic transformations, hence we propose to learn a subspace determined by such transformations from data and design a new ROM for transport problems.

报告时间：2024.03.20上午10:40-11:40

报告地点：理学楼609室

报告人简介：彭志超，现任香港科技大学数学系助理教授一职。2015年在北京大学取得学士学位，2020年在美国伦斯勒理工大学取得博士学位，曾任美国密歇根州立大学访问助理教授。主要研究兴趣是偏微分方程数值解，模型约化和数据鹅分析。