Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

Abstract

In this article, we present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex shedding patterns. We consider the flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed DL-ROM methodology relies on a three-dimensional convolutional recurrent autoencoder network (3D CRAN) to extract the low-dimensional flow features from the full-order snapshots in an unsupervised manner. The low-dimensional features are evolved in time using a long short-term memory-based recurrent neural network and reconstructed back to the full-order as flow voxels. These flow voxels are introduced as static and uniform query probes in the point cloud domain to reduce the unstructured mesh complexity while providing convenience in the 3D CRAN training. We introduce a novel procedure to recover the interface description and the instantaneous force quantities from these 3D flow voxels. To evaluate the 3D flow reconstruction and inference, the 3D CRAN methodology is first applied to an external flow past a static sphere at the single Reynolds number of Re = 300. We provide an assessment of the computing requirements in terms of the memory usage, training, and testing cost of the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a symmetry-breaking flow regime (280 [Formula: see text] Re [Formula: see text] 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complex 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the flow regime nearly 20 times faster than the parallel full-order model and predicts this flow regime in time with a reasonable accuracy. Based on the predicted flow fields, the network demonstrates an [Formula: see text] accuracy of 98.58% for the drag and 76.43% for the lift over the sphere in this flow regime. The proposed framework aligns with the development of a digital twin for 3D unsteady flow field and instantaneous force predictions with variable Re-based effects.

Dynamics of cavity structures and wall-pressure fluctuations associated with shedding mechanism in unsteady sheet/cloud cavitating flows

“…The data-driven methods of modal decomposition approaches called proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are becoming more and more popular recently to provide physical insights into the cavitation instabilities (Gupta & Jaiman, 2022; Liu, Long, Wu, Huang, & Wang, 2021) instead of observing the evolution of cavity on acquired high-speed images, to explore these abundant spatial-temporal features of coherent structures and the associated dynamics in cavitation flows, especially in the sheet/cloud cavitation regime. For example, Prothin, Billard, and Djeridi (2016) experimentally investigated the sheet/cloud cavitation instabilities around a NACA0015 foil at high Reynolds number using POD and DMD, and pointed out the occurrence of three-dimensional (3-D) effects due to the re-entrant jet instabilities or due to the propagating shockwave mechanism at the origin of the shedding process of the cavitation cloud.…”

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

“…Regarding IROMs, the exact form of the underlying partial differential equations (PDEs) is essential to generate simplified models from high fidelity snapshots [27], in an ordered database called snapshot matrix [28]. Proper orthogonal decomposition (POD) approximates the intrinsic dimensions of the HFM solutions by utilizing linear algebra techniques such as principal component analysis, and singular value decomposition (SVD) [29,30].…”

“…In recent years, NIROMs DL-based have been the subject of several studies aiming to overcome the limitations of the linear projections methods [28], by recovering non-linear, low-dimensional manifolds [36,42]. Various methodologies have been proposed, including supervised and unsupervised DL techniques, to identify low-dimensional manifolds and nonlinear dynamic behaviors [49].…”

Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics

“…In recent years, machine learning has witnessed a resurgence owing primarily to the enormous success of deep learning models in a wide range of applications 22 . One such application is reduced-order modeling, in which a deep learning model is used as a black box technique to approximate a physical system 9,14 . Deep neural networks, one of the most popular deep learning models, have proven to be an effective method for modeling physical systems, e.g.…”

“…Explicit physical constraints in the loss function necessitate numerical solution of a partial differential equation which brings back the computational infeasibility of numerical methods 21,36 . In recent body of works 9,14,27 , deep neural networks have been shown to model complex fluid-structure interaction and wave propagation phenomenon without relying on explicit physical constraints or inductive biases in the loss function. Convolutional recurrent autoencoder network (CRAN) 3,4,8 , is a deep neural network that can be effective for data-driven model reduction and learning of nonlinear partial differential equations.…”