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

In this paper, we employed a transfer learning technique to predict the Nusselt number for natural convection flows in enclosures. Specifically, we numerically simulated a benchmark problem in square enclosures described by the Rayleigh and Prandtl numbers using the finite volume method. Given that the ideal grid size depends on the value of these parameters, we performed our simulations using a combination of different grid systems. This allowed us to train an artificial neural network in a cost-effective manner. We adopted two approaches to this problem. First, we generated a multi-grid training dataset that included both the Rayleigh and Prandtl numbers as input variables. By monitoring the training losses for this dataset, we were able to detect any significant anomalies that stemmed from an insufficient grid size. We then revised the grid size or added more data points to denoise the dataset and transferred the learning from our original dataset to build a computational metamodel that predicts the Nusselt number. Furthermore, we sought to endow our neural network model with the ability to account for additional input features. Therefore, in our second approach, we applied a deep neural network architecture for transfer learning to this problem. Initially, we trained a neural network with a single input feature (Rayleigh), and then, extended the network to incorporate the effects of a second feature (Prandtl). This learning framework can be applied to other systems of natural convection in enclosures that presumably have higher physical complexity, while bringing the computational and training costs down.