Direct numerical simulation of Rayleigh–Bénard convection based on physics-informed neural networks with transfer learning

Rayleigh–Bénard (RB) convection, characterized by a fluid layer with bottom heating and top cooling, serves as a fundamental model system in fluid dynamics research, serves as an essential paradigm for studying thermally driven flows, offering fundamental understanding of heat transfer, fluid mixing, and turbulent transition processes that occur widely in nature and industrial systems. This study introduces the application of Physics-Informed Neural Networks (PINNs) augmented with transfer learning techniques. Using transfer learning, our aim is to take advantage of the knowledge gained from training PINNs on a Ra condition to improve predictions for other Ra values. Preliminary results show that transfer learning-enhanced PINNs successfully capture the convective regime while avoiding convergence to steady-state solutions, enabling efficient prediction across varying Rayleigh (Ra) numbers without requiring full retraining. Furthermore, different ways of transferring models are also proposed to explore the feasibility of knowledge transfer across different natural convection configurations, including cases with varying inclination angles and Prandtl (Pr) numbers. The effective incorporation of transfer learning into PINNs have demonstrated promising capabilities for RB convection modeling, suggesting several key areas for future investigation. Further advanced transfer strategies suited to particular physical systems and conditions can be investigated as PINNs develop.