Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

Bukka, Sandeep Reddy; Gupta, Rachit; Magee, Allan; Jaiman, Rajeev K.

doi:10.1063/5.0030137

Cited by 71 publications

(49 citation statements)

References 45 publications

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“…2020; Xu & Duraisamy 2020; Bukka et al. 2021). Since a few studies have also recently recognized the challenges of the current form of CNN-AE for turbulence (Brunton, Hemati & Taira 2020; Fukami et al.…”

Section: Discussionmentioning

confidence: 99%

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

et al. 2021

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We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm and the adaptive least absolute shrinkage and selection operator which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$ , its transient process and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high-dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy-based modelling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyse high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

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Section: Discussionmentioning

confidence: 99%

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

et al. 2021

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“…Such hybrid architectures consider spatio-temporal domain knowledge and achieve data-driven time series predictions. Recently proposed POD-based DL-ROMs are the POD-CNN by Miyanawala and Jaiman 40 , the POD-RNN by Bukka et al 7 , the POD-enhanced autoencoders by Fresca and Manzoni 17 . These hybrid architectures have been demonstrated for 2D bluff body flows with and without fluid-structure interaction.…”

Section: A Deep Leaning-based Reduced Order Modelingmentioning

confidence: 99%

“…Many promising approaches have been established in the research community for a synergistic coupling of deep learning and physics-based models 7,9 . These models are trained to represent a full or partial parametrization of a forward process to reduce computational costs while emulating physical laws.…”

Section: B Review Of Physics-based Deep Leaningmentioning

confidence: 99%

“…Likewise, Snachez et al 51 and Pfaff et al 46 utilized graph neural networks to represent the state of a physical system as nodes in a graph and compute the dynamics by learning messagepassing signals. The third category in the physics-based deep learning involves the development of the hybrid DL-ROMs that take into account the spatial and temporal domain knowledge in neural networks 7,17,19,40 . We refer to such DL-ROM frameworks as physics-based because they incorporate physical interpretability via proper orthogonal decomposition and its variants.…”

Section: B Review Of Physics-based Deep Leaningmentioning

confidence: 99%

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

Gupta,

Jaiman

2021

Preprint

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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 (LSTM-RNN) 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 analyze a novel procedure to recover the interface description and the instantaneous force quantities from these 3D flow voxels. The 3D CRAN-based DL-ROM methodology is first applied to an external flow past a static sphere at single Reynolds number (Re) of Re = 300 to test the 3D flow reconstruction and inference. We provide an assessment of the computing requirements in terms of the memory usage, training costs and testing times associated with the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a complicated symmetry-breaking flow regime (280 ≤ Re ≤ 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complicated 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the complicated flow regime nearly 20 times faster than the parallel full-order model and predicts this flow regime in time with an excellent to good accuracy. Based on the predicted flow fields, the network demonstrates an R 2 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 effects.

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“…This latter defines a sparse representation through a linear combination of selected functions, and has been used for data-driven forecasting in fluid dynamics [49]. RNNs have been considered in [50,51] to evolve lowdimensional states of unsteady flows, exploiting either POD or a convolutional recurrent autoencoder to extract low-dimensional features from snapshots. DL algorithms have also been used in [52] to describe the reduced trial manifold where the approximation is sought, then relying on a minimum residual formulation to derive the ROM-hence, still requiring the assembling and the solution of a ROM as in traditional POD-Galerkin ROMs.…”

mentioning

confidence: 99%

Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models

Fresca

Manzoni

2021

Fluids

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Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov–Galerkin projections) if a mixed velocity–pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid–structure interactions entails even greater difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning, in a nonintrusive way, both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD, enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid–structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.

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Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

Cited by 71 publications

References 45 publications

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

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

Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models

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