Unsteady reduced-order model of flow over cylinders based on convolutional and deconvolutional neural network structure

Peng, Jiang-Zhou; Chen, Siheng; Aubry, Nadine; Chen, Zhihua; Wu, Wei‐Tao

doi:10.1063/5.0030867

Cited by 49 publications

(7 citation statements)

References 16 publications

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“…However, applying sequence models to predict high-dimensional systems remains a challenge due to their high memory overhead. Dimensionality reduction techniques, such as CNN autoencoders [33,32,26,22,29,16,11,27], POD [44,48,5,31,18,8,47,10], or Koopman operators [24,9,14] can be used to construct a lowdimensional latent space. The auto-regressive sequence model then operates on these linear (POD modes) or nonlinear (CNNs) latents.…”

Section: Related Workmentioning

confidence: 99%

Predicting Physics in Mesh-reduced Space with Temporal Attention

Han¹,

Han²,

Pffaf³

et al. 2022

Preprint

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Graph-based next-step prediction models have recently been very successful in modeling complex high-dimensional physical systems on irregular meshes. However, due to their short temporal attention span, these models suffer from error accumulation and drift. In this paper, we propose a new method that captures long-term dependencies through a transformer-style temporal attention model. We introduce an encoder-decoder structure to summarize features and create a compact mesh representation of the system state, to allow the temporal model to operate on a low-dimensional mesh representations in a memory efficient manner. Our method outperforms a competitive GNN baseline on several complex fluid dynamics prediction tasks, from sonic shocks to vascular flow. We demonstrate stable rollouts without the need for training noise and show perfectly phase-stable predictions even for very long sequences. More broadly, we believe our approach paves the way to bringing the benefits of attention-based sequence models to solving high-dimensional complex physics tasks.

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Section: Related Workmentioning

confidence: 99%

Predicting Physics in Mesh-reduced Space with Temporal Attention

Han¹,

Han²,

Pffaf³

et al. 2022

Preprint

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show abstract

“…Recent advances in scientific machine learning (SciML) and ever-growing data availability open up new possibilities to tackle these challenges. In the past few years, various deep neural networks (DNNs) have been designed to learn the spatiotemporal dynamics in latent spaces enabled by proper orthogonal decomposition (POD) [1][2][3][4][5][6] or convolutional encoding-decoding operations [7][8][9][10][11][12][13]. In particular, fast neural simulators based on graph neural networks (GNN) have been proposed and demonstrated to predict spatiotemporal physics on irregular domains with unstructured meshes [14,15].…”

Section: Introductionmentioning

confidence: 99%

Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning

Liu¹,

Sun²,

Wang³

2022

Preprint

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Although recent advances in deep learning (DL) have shown a great promise for learning physics exhibiting complex spatiotemporal dynamics, the high training cost, unsatisfying extrapolability for long-term predictions, and poor generalizability in out-of-sample regimes significantly limit their applications in science/engineering problems. A more promising way is to leverage available physical prior and domain knowledge to develop scientific DL models, known as physics-informed deep learning (PiDL). In most existing PiDL frameworks, e.g., physicsinformed neural networks, the physics prior is mainly utilized to regularize neural network training by incorporating governing equations into the loss function in a soft manner. In this work, we propose a new direction to leverage physics prior knowledge by baking the mathematical structures of governing equations into the neural network architecture design. In particular, we develop a novel PDE-preserved neural network (PPNN) for rapidly predicting parametric spatiotemporal dynamics, given the governing PDEs are (partially) known. The discretized PDE structures are preserved in PPNN as convolutional residual network (ConvResNet) blocks, which are formulated in a multi-resolution setting. This physics-inspired learning architecture design endows PPNN with excellent generalizability and long-term prediction accuracy compared to the state-of-the-art blackbox ConvResNet baseline. The effectiveness and merit of the proposed methods have been demonstrated over a handful of spatiotemporal dynamical

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“…In both studies, a signed distance function (SDF) is proposed to represent the geometry of the problem. Subsequently, the authors also used CNN structure to rapidly predict the steady flow [24] and unsteady flow [25] over objects with arbitrary geometry and various boundary conditions where the input matrix is composed of the nearest wall signed distance function (NWSDF). The results of all the studies show the high accuracy and efficiency of the proposed network model, indicating the geometry adaptive ability of the CNN-based reduced order model.…”

Section: Introductionmentioning

confidence: 99%

Thermal Performance in Convection Flow of Nanofluids Using a Deep Convolutional Neural Network

et al. 2022

Self Cite

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This study develops a geometry adaptive, physical field predictor for the combined forced and natural convection flow of a nanofluid in horizontal single or double-inner cylinder annular pipes with various inner cylinder sizes and placements based on deep learning. The predictor is built with a convolutional-deconvolutional structure, where the input is the annulus cross-section geometry and the output is the temperature and the Nusselt number for the nanofluid-filled annulus. Profiting from the proven ability of dealing with pixel-like data, the convolutional neural network (CNN)-based predictor enables an accurate end-to-end mapping from the geometry input and the desired nanofluid physical field. Taking the computational fluid dynamics (CFD) calculation as the basis of our approach, the obtained results show that the average accuracy of the predicted temperature field and the coefficient of determination R2 are more than 99.9% and 0.998 accurate for single-inner cylinder nanofluid-filled annulus; while for the more complex case of double-inner cylinder, the results are still very close, higher than 99.8% and 0.99, respectively. Furthermore, the predictor takes only 0.038 s for each nanofluid field prediction, four orders of magnitude faster than the numerical simulation. The high accuracy and the fast speed estimation of the proposed predictor show the great potential of this approach to perform efficient inner cylinder configuration design and optimization for nanofluid-filled annulus.

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Unsteady reduced-order model of flow over cylinders based on convolutional and deconvolutional neural network structure

Cited by 49 publications

References 16 publications

Predicting Physics in Mesh-reduced Space with Temporal Attention

Predicting Physics in Mesh-reduced Space with Temporal Attention

Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning

Thermal Performance in Convection Flow of Nanofluids Using a Deep Convolutional Neural Network

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