Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Traditional macroscopic non-Fourier heat conduction models often rely on small perturbation methods, limiting their accuracy at high Knudsen numbers and for nonequilibrium transport.
• Existing models struggle to capture complex thermal behaviors in highly nonequilibrium or ballistic heat conduction scenarios.

Purpose of the Study:

• To develop a novel data-driven deep learning strategy for macroscopic non-Fourier heat conduction modeling.
• To overcome the limitations of traditional perturbation-based methods, particularly for highly nonequilibrium and ballistic transport regimes.

Main Methods:

• Introduced the mechanism-data fusion method, integrating nonequilibrium thermodynamics with deep learning.
• Leveraged the conservation-dissipation formalism (CDF) and dual-dissipative variables to derive interpretable partial differential equations.
• Utilized a training strategy informed by phonon Boltzmann transport equation data and an inner-step operation for discrete-to-continuous system bridging.

Main Results:

• The developed model demonstrates excellent predictive capabilities across diffusive, hydrodynamic, and ballistic heat conduction regimes.
• The approach shows robustness and precision, even when dealing with discontinuous initial conditions.
• The mechanism-data fusion method offers a more comprehensive approach to non-Fourier heat conduction compared to traditional methods.

Conclusions:

• The data-driven deep learning approach combined with nonequilibrium thermodynamics provides a powerful and versatile tool for modeling non-Fourier heat conduction.
• This method successfully captures complex thermal transport phenomena beyond the limitations of small perturbation expansions.
• The model's ability to handle diverse regimes and initial conditions highlights its potential for advanced thermal management applications.