报告题目：A Mechanism-Data Fusion Method for Modeling Heat Conduction
报告人：赵进老师（首都师范大学交叉科学研究院特聘副研究员）
时间：2025年5月15日 10:00 - 12:00
地点：数学学院203报告厅
报告摘要：
We provide a brief overview of the modeling process, from Newton’s molecular dynamics to the Boltzmann equation and ultimately the macroscopic Navier-Stokes equations. We then introduce our Mechanism-Data Fusion Method (MDFM) for modeling heat conduction with two dissipative variables, combining the mathematical rigor of physical laws, the adaptability of machine learning, and the solvability of conventional numerical methods. Using the Conservation-Dissipation Formalism, we derive a system of first-order hyperbolic partial differential equations for heat conduction that naturally adheres to the first and second laws of thermodynamics. We train the unknown functions in this system with deep neural networks and propose a novel technique, the Inner-Step Operation, to bridge the gap between the discrete and continuous forms. Extensive numerical experiments show that the model accurately predicts heat conduction across diffusive, hydrodynamic, and ballistic regimes, and outperforms the Guyer-Krumhansl model in terms of accuracy over a wider range of Knudsen numbers.
报告人简介：赵进，首都师范大学交叉科学研究院特聘副研究员，他的研究方向包含数值方法，数学建模，机器学习等，包括将机器学习应用到偏微分方程数值解和数学建模中。相关工作发表在SISC, JCP, PRE, INT J HEAT MASS TRAN等权威学术期刊
