摘要：In this paper, we employed a transfer learning technique to predict the Nusselt number for natural convection flows in enclosures. Specifically, we considered the benchmark problem of a two-dimensional square enclosure with insulated horizontal walls and constant-temperature vertical walls. The Rayleigh and Prandtl numbers are sufficient parameters to simulate this problem numerically. We adopted two approaches to this problem: Firstly, we made use of a multi-grid dataset in order to train our artificial neural network in a cost-effective manner. By monitoring the training losses for this dataset, we detected 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 aimed to endow our metamodel with the ability to account for additional input features by performing transfer learning using deep neural networks. We trained a neural network with a single input feature (Rayleigh number) and extended it to incorporate the effects of a second feature (Prandtl number). We also considered the case of hollow enclosures, demonstrating that our learning framework can be applied to systems with higher physical complexity, while bringing the computational and training costs down.
