Mechanism-Data Fusion Method for Modeling Heat Conduction
数学专题报告
报告题目(Title)：Mechanism-Data Fusion Method for Modeling Heat Conduction
报告人(Speaker)：赵进 (首都师范大学)
地点(Place)：后主楼1124
时间(Time)：2023年6月22日(周四), 15:00-16：00
邀请人(Inviter)：潘亮
报告摘要
A mechanism-data fusion method (MDFM) is proposed for modeling heat conduction with two-dissipative variables. This method enjoys mathematical rigor from physical laws, adaptability from machine learning, and solvability from conventional numerical methods. Specifically, we use the conservation-dissipation formalism (CDF) to derive a system of first-order hyperbolic partial differential equations (PDEs) for heat conduction, which naturally obeys the first and second laws of thermodynamics. Next, we train the unknown functions in this PDE system with deep neural networks. Moreover, we propose a novel method, the Inner-Step operation (ISO), to narrow the gap from the discrete form to the continuous system. Lots of numerical experiments are conducted to show that the proposed model can well predict the heat conduction in diffusive, hydrodynamic and ballistic regimes, and the model displays higher accuracy under a wider range of Knudsen numbers than the famous Guyer-Krumhansl (G-K) model.
主讲人简介
赵进，首都师范大学交叉科学研究院特聘副研究员。曾在北京大学数学科学学院从事博士后研究工作，获得中国博士后面上资助一等。中国工程物理研究院博士。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。
