Automated framework for data-based modeling of filtered drag for coarse-grained simulations of fluidized beds*

Data-based approaches relying on Artificial Neural Networks (ANN) have recently been proposed to model the drag correction factor in coarse-grained simulations of fluidized beds, showing excellent agreement with the physics, especially compared to simulations employing crude analytical models. However, the accuracy of ANNs is largely influenced by the chosen architecture and hyperparameters (activation functions, number of epochs, learning rate etc.), and no defined rules are available for the user to set these a priori. Therefore, the prediction accuracy becomes largely dependent on user expertise in hand-tuning hyperparameters via grid or random searches. In this work, an automated framework to train ANN-based models for the correction coefficient of gas-particle drag is proposed and validated a posteriori. A probabilistic model is first constructed via Bayesian optimization to converge, in an unsupervised fashion, to the optimal architecture and hyperparameters for the ANN. Three different acquisition functions for the design space exploration are tested (i.e., probability of improvement, expected improvement, and lower confidence bound), and their influence on the networks' size and accuracy of the simulations is assessed. Finally, a semi-analytical linear formulation to model the dependence of the drag correction factor from the pressure gradient (for different conditions of void fraction and slip velocity) is derived by means of the ANN predictions.