Extracting Fundamental Parameters of 2-D Natural Thermal Convection Using Convolutional Neural Networks

The Lattice Boltzmann Method (LBM) is an approach for modelling mesoscopic fluid flow and heat transfer, based on modelling distributions of particles moving and colliding on a lattice. Based on a perturbative formulation of the Boltzmann Equation, it scales to the macroscopic Navier Stokes equation[1]. We simulate natural thermal convection via LBM in a 2-D rectangular box being heated from below, cooled from above[2], and use the results as training, testing and generalization datasets to build a deep learning model. GoogLeNet, a convolutional neural network (CNN)[3], is used to classify the simulation results based on two parameters: Rayleigh (Ra) and the Prandtl (Pr) numbers. For each fixed Pr from 1 to 128, we extract Ra with accuracy around 90% from a single snapshot. For a fixed Ra, the classification of Pr shows greater uncertainties. Finally, we test the method performance from small randomly placed snapshots of a larger convecting domain. This approach has a great potential for industrial application like electronic equipment cooling or scientific research on Earth and in Space.

References

[1] Sharma, K. V., Straka, R., & Tavares, F. W. (2020). Current status of Lattice Boltzmann Methods applied to aerodynamic, aeroacoustic, and thermal flows. Progress in Aerospace Sciences, 115, 100616.

[2] Mora, Peter, Gabriele Morra, and David A. Yuen. "A concise python implementation of the lattice Boltzmann method on HPC for geo-fluid flow." Geophysical Journal International 220.1 (2020): 682-702.

[3] Szegedy, Christian, et al. "Going deeper with convolutions." Proceedings of the IEEE conference on computer vision and pattern recognition. 2015.