Hybrid Machine Learning based Reduced-Order Modeling of Complex Flows

Abstract

In nature, most dynamical systems are governed by chaos. In fluid mechanics, chaos manifests in the form of turbulence, characterized by abrupt changes in the flow field. These chaotic changes in fluid streams impose hydrodynamic forces on the structures they interact with causing them to vibrate. If the frequency of the imposed vibratory forces matches the natural frequency of the structure, the resulting resonance can cause a drastic increase in the amplitude of vibration, often leading to structural failure. The research performed in this work is motivated by a desire to model flow around bluff bodies that ultimately results in vortex-induced vibrations (VIV). This aim is achieved by following the trajectory of conventional reduction models and improving upon their performance. The improvement is brought about in three phases. In the first phase, alternative solution strategies to direct numerical simulation are evaluated because of the considerable computational expense of full-order models. A Galerkin projection based model reduction framework using proper orthogonal decomposition (POD) basis is selected as an appropriate substitute to full-order models. Additionally, the shortcomings Galerkin models are addressed and conventional improvement strategies such as closure modeling are investigated. In the second phase, several machine learning (ML) based solution strategies in fluid mechanics are evaluated in terms their accuracy and solution expense. To that end, both deep learning full-order models and reduction models are considered. Based on the analysis presented, a hybrid reduction framework, through the integration of proper orthogonal decomposition and machine learning is suggested to provide the best trade-off between solution accuracy and computational expense. In the third and final phase, a machine learning based hybrid reduced-order modeling framework is developed with an aim of providing a complete model reduction framework. The model utilizes machine learning tools to upscale a given number of temporal coefficients to account for the effect of the truncated dynamics during the POD process, thus eliminating the need for conventional closures. Secondly, the proposed model is capable of predicting future states of the temporal coefficients we well, analogous to integrating the Galerkin reduced system. The proposed model is tested on both in-sample and out-of-sample data sets. Spatial modes of in-sample data are taken from the DNS set of POD basis used to the train the ML model. Whereas, out-of-sample spatial dynamics viii is obtained via Grassmann manifold interpolation using the available set of DNS modes. Finally, the model is tested for its ability to reconstruct velocity and pressure dynamics in both two-dimensional and three-dimensional scenarios, representing periodic and chaotic dynamics, respectively. Moreover, the proposed model is shown to have a similar computational expense as POD while showing better accuracy, resulting in a more efficient model reduction framework. In addition, the model has the ability to reproduce and predict turbulent hydrodynamic forces, a crucial requirement that enables the application of data-driven control. Therefore, the proposed ML model is established as a valid and accurate reduced-order modeling framework.