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In this paper, we employed a transfer learning technique to predict theNusselt number for natural convection flows in enclosures. Specifically, weconsidered the benchmark problem of a two-dimensional square enclosure withisolated horizontal walls and vertical walls at constant temperatures. TheRayleigh and Prandtl numbers are sufficient parameters to simulate this problemnumerically. We adopted two approaches to this problem: Firstly, we made use ofa multi-grid dataset in order to train our artificial neural network in acost-effective manner. By monitoring the training losses for this dataset, wedetected any significant anomalies that stemmed from an insufficient grid size,which we further corrected by altering the grid size or adding more data.Secondly, we sought to endow our metamodel with the ability to account foradditional input features by performing transfer learning using deep neuralnetworks. We trained a neural network with a single input feature (Rayleigh)and extended it to incorporate the effects of a second feature (Prandtl). Wealso considered the case of hollow enclosures, demonstrating that our learningframework can be applied to systems with higher physical complexity, whilebringing the computational and training costs down.

A transfer learning metamodel using artificial neural networks applied to natural convection flows in enclosures