Machine learning closures for model order reduction of thermal fluids

We put forth a data-driven closure modeling approach for stabilizing projection based reduced order models for the Bousinessq equations. The effect of discarded modes is taken into account using a machine learning architecture consisting of a single hidden layer feed-forward artificial neural network to achieve robust stabilization with respect to parameter changes. For training our network architecture, we implement an extreme learning machine strategy to utilize fast learning speeds and excellent generalized predictive capabilities for underlying statistical trends. The architecture is then deployed to recover reduced order model dynamics of flow phenomena which are not used in our training data set. A two-dimensional differentially heated cavity flow is used to demonstrate the advantage of the proposed framework considering a large set of modeling parameters. It is observed that the proposed closure strategy performs remarkably well in stabilizing the temporal mode evolution and represents a promising direction for closure development of predictive reduced order models for thermal fluids.