Multi-fidelity prediction of spatiotemporal fluid flow
Sudeepta Mondal, Soumalya Sarkar
Abstract
Data-driven prediction of spatiotemporal fields in fluid flow problems has received significant interest lately. However, the scarcity of data often plagues the accuracy of the prevalent approaches, particularly in situations where the cost associated with the generation of high-fidelity data is prohibitively expensive. Moreover, the data sources in many spatiotemporal fluid flow problems present a hierarchy of fidelities with respect to their computational cost/accuracy, such that the higher fidelity sources are more accurate and also more expensive than the low-fidelity sources. This article presents a novel multi-fidelity spatiotemporal modeling approach whereby the lower fidelity data source for a dynamical process is gainfully utilized in increasing the accuracy of predicting the higher fidelity fields, thereby reducing the overhead of high-fidelity simulations for data-driven prediction. The methodology is based on non-intrusive reduced order modeling using deep convolutional autoencoders, combined with a latent-space evolution framework based on multi-fidelity Gaussian processes. This framework results in probabilistic spatiotemporal predictions for unknown operating conditions of the dynamical system, which provides the end user with quantified levels of uncertainties associated with the data-driven predictions. The framework is validated on a prototypical fluid flow problem of interest: two-dimensional incompressible viscous flow around a cylinder.