Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Associate Professor Jin Zhao, Capital Normal University
Inviter:	Associate Professor Jie Xu
Title:	Mechanism-Data Fusion Method for Modeling Heat Conduction
Language:	Chinese
Time & Venue:	2023.08.07 09:30-10:30 Z311
Abstract:	In this talk, we present a mechanism-data fusion method (MDFM) 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. We conduct lots of numerical experiments which show that the proposed model can well predict the heat conduction in diffusive, hydrodynamic and ballistic regimes. This is a joint work with Leheng Chen and Chuang Zhang.