This study presents a deep learning (DL) neural network hybrid data-driven method that is able to predict turbulence flow velocity field. Recently many studies have reported the application of recurrent neural network (RNN) methods, particularly the Long short-term memory (LSTM) for sequential data. The airflow around the objects and wind speed are the most presented with different hybrid architecture. In some of them, the data series is used with the known equation, and the data is firstly generated. Data series extracted from Computational Fluid Dynamics (CFD) have been used in many cases. This work aimed to determine a method with raw data that could be measured with devices in the airflow, wind tunnel, water flow in the river, wind speed and industry application to process in the DL model and predict the next time steps. This method suggests spatialtemporal data in time series, which matches the Lagrangian framework in fluid dynamics. Gated Recurrent Unit (GRU), the next generation of LSTM, has been employed to create a DL model and forecasting. Time series data source is from turbulence flow has been generated in a laboratory and extracted via 2D Lagrangian Particle Tracking (LPT). This data has been used for the training model and to validate the prediction in the suggested approach. The achievement via this method dictates a significant result and could be developed.This work was performed in the Center of Excellence (CoE) Research on AI and Simulation Based Engineering at Exascale (RAISE) and the EuroCC projects receiving funding from EU’s Horizon 2020 Research and Innovation Framework Programme under the grant agreement no.951733 and no. 951740 respectively.Peer Reviewe

Bouhlali, Lahcen

Hassanian, Reza

Riedel, Morris

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The Capability of Recurrent Neural Networks toPredict Turbulence Flow via SpatiotemporalFeaturesReza Hassanian∗, Morris Riedel∗,†, Lahcen Bouhlali‡∗The Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland, Reykjavik, Iceland†Juelich Supercomputing Centre, Germany‡Department of Engineering, School of Technology, Reykjavik University, Reykjavik, Iceland∗seh@hi.is, †morris@hi.is, ‡lahcen09@ru.isAbstract—This study presents a deep learning (DL) neuralnetwork hybrid data-driven method that is able to predict tur-bulence flow velocity field. Recently many studies have reportedthe application of recurrent neural network (RNN) methods,particularly the Long short-term memory (LSTM) for sequentialdata. The airflow around the objects and wind speed are the mostpresented with different hybrid architecture. In some of them,the data series is used with the known equation, and the data isfirstly generated. Data series extracted from Computational FluidDynamics (CFD) have been used in many cases. This work aimedto determine a method with raw data that could be measuredwith devices in the airflow, wind tunnel, water flow in the river,wind speed and industry application to process in the DL modeland predict the next time steps. This method suggests spatial-temporal data in time series, which matches the Lagrangianframework in fluid dynamics. Gated Recurrent Unit (GRU), thenext generation of LSTM, has been employed to create a DLmodel and forecasting. Time series data source is from turbulenceflow has been generated in a laboratory and extracted via 2DLagrangian Particle Tracking (LPT). This data has been used forthe training model and to validate the prediction in the suggestedapproach. The achievement via this method dictates a significantresult and could be developed.Index Terms—Recurrent Neural Network, Unsteady Flow,Deep LearningI. INTRODUCTIONTurbulence is observed in the most natural and artificialphenomena [1] [2]. Water in the waterfall, airflow in the wind,smoke from a chimney, and airflow around the objects areexamples from the environment [1]. The industry cases are theflow in the engine mixing chamber; two working flows insidethe heat exchanger, and airflow around the airplane and car [1][3] [4] [5]. In large-scale turbulence, solar flare, oceanic andatmospheric flow are other giant emanations that influence ourlives [2]. The turbulence flow almost everywhere [1]. Turbu-lence flow is chaotic, nonrepeatable, and random, and it is wellThis work was performed in the Center of Excellence (CoE) Research onAI and Simulation Based Engineering at Exascale (RAISE) and the EuroCCprojects receiving funding from EU’s Horizon 2020 Research and InnovationFramework Programme under the grant agreement no.951733 and no. 951740respectively.addressed that the statistics aspect of the flow is applicable[1]. On the other hand, Computational Fluid Dynamics (CFD)is a leading traditional numerical approach to dealing withnonlinear fluid dynamics phenomena such as turbulence flow.Direct Numerical Method (DNS) and Large Eddy Simulation(LES) are two capable and accurate methods to resolve theturbulent flow problems. But, from the computational cost,they are costly. High-performance computation (HPC) is anessential factor for all solutions in DNS and LES. Simulationfor many types of turbulence problems is almost impossible onthe actual scale because of the limitation in the computation.Scientists have efforts to create similar scale problems tonatural phenomena. However, we are still far from solvingproblems with extensive size. In many CFD applications, itis required to validate the solution with empirical data, is ananother limitation. These constraints illustrate a reliable toolis necessary to overcome the above-called obstacles. Machinelearning (ML) based on Artificial Intelligence (AI) has becomean important key to encountering nonlinear phenomena. Deeplearning (DL) is a capable approach in ML and is ableto extract the hidden features from complex and nonlineardynamic systems [6] [7]. Recurrent neural network (RNN) isa type of neural network especially appropriate for sequentialdata such as time series [6]. An RNN is a neural networkcomposed of an individual hidden layer with a feedback loopin which the hidden layer output with the current input isreturned to the hidden layer [6]. RNN network defines thetemporal relationship because of sequential input data, andthree weight matrices and two biases characterize it. RNNscan almost not train sequence data with long-range temporaldependencies because the vanishing gradients problem exists[6]. Long short-term memory (LSTM) network was developedand suggested in 1995 [8]. LSTM applies a gating structure tocontrol the transients of the recurrent connectors and can dealwith the vanishing gradient issue. Moreover, it is able to modellonger temporal dependencies rather than standard RNNs [6].Recently, LSTM has been employed in many studies in orderto model time series prediction. The interest in this method hasalso increased in the fluid dynamics area. Vinuesa et al. [6]have used LSTM to predict the turbulence shear flow. Veisi etal. [7] used LSTM hybrid model prediction for unsteady flows.LSTM Potential has been led to hybrid models such as convo-lutional neural network (CNN)–LSTM, Autoencoders–LSTM,and LSTM/RNN [9]. Gated recurrent unit (GRU) [10] is avariant of LSTM which has fewer parameters than LSTM,and the training rate is faster [9]. In GRU, the forget gateand input gate in LSTM are replaced with only one updategate [9]. GRU is required fewer data to train the model,therefore gaining a similar performance in multiple tasks withless computation [9]. Recently GRU has been employed toforecast wind speed and predicts electricity demand [10] [11][12]. Most fluid flow studies that were applied ML/DL arecomposed of data extracted from CFD studies’ known equa-tions. On the other hand, many works included preliminarysteps to do autoencoder to extract the main features, such as,proper orthogonal decomposition (POD), dynamic mode de-composition (DMD), and well-known reduced order methods(ROMs) [7] [13] [14] [15]. In the ML/DL context, there is acapability to determine a training method with raw data fromthe Lagrangian framework velocity field involving spatial andtemporal features. In many applications of industry, researchand experiment, it is possible to measure the velocity fielddirectly or indirectly via devices such as constant temperatureanemometer (CTA), flowmeter (and obtain the velocity), pitottube, laser doppler anemometry (LDA), and light detectionand ranging (LIDAR). This study introduces a method to usetime series data consisting of velocity components and positionin 2D coordinate to train the GRU model and evaluate theprediction in future time. Hence, this paper is organized asfollows. The applied theory is presented in Section II . InSection III , the method is introduced. Section IV discussesthe result, and the conclusions are presented in Section V .II. THEORYA. Lagrangian Framework in fluid dynamicsLagrangian framework is a description of the motion fluid,involves keeping track of the position vector and velocityvector of each point of flow which it is called fluid particle[1] [16]. A fluid particle is a point that moves with the localfluid velocity, therefor it specifies the position at time t of fluidparticle [16]. The definition of fluid particle mathematically is[1]:xi = xi(t, xi,0) , i = 1, 2, 3 (1)Ui = Ui(t, x1(t, x1,0), x2(t, x2,0), x3(t, x3,0)) , i = 1, 2, 3(2)Where (1) and (2) determines the fluid particle positionand velocity in 3D coordinates respectively. x is the position,U is the velocity, t is the time and denote i specifies thevector component. Based on the Lagrangian definition, forfluid particle there is a time series data which specify a positionand velocity at particular time. Particularly in turbulenceflow which has not known equation and it is investigated instatistics, these time series data available and appropriate touse.B. Gated Recurrent Unit (GRU)From the DL method, it is well known that RNNs canperform prediction for sequence data via Long Short TimeMemory (LSTM). Gated Recurrent Unit (GRU) [17] is a next-generation defemination from LSTM with a bit distinctionin the model architecture. Literature reports that GRU iscomparable in performance is considerably faster to computethan LSTM and has a streamlined model [18]. GRU cellthat is displayed in Fig. 1, is composed of a hidden state,reset gate, and update gate. We can control how much ofthe previously hidden state might be remembered from thereset gate. On the other hand, via the update gate, we canunderstand how much of the new hidden state is just a copy ofthe old hidden state. This architecture in the GRU establishestwo significant features: the reset gate captures short-termdependencies in sequences, and the update gate receives long-term dependencies in sequences [17].Fig. 1. Gated Recurrent Unit (GRU) cellIII. METHODOLOGYA. Velocity time series dataThis study has designed and applied a suggested hybridmodel based on time series vector data for velocity. The spatialand temporal data extracted from 2D Lagrangian ParticleTracking (LPT) have been recorded in the laboratory. Theflow is turbulence with straining deformation generated inthe experiment. Data is included time, velocity in x and ydirections, and position in x and y coordinates. Therefore, wehave corresponding velocity and position with a specific timein this time series. In the suggested model, since the velocityis with two components in the x and y direction, we carriedon the model for every component individually. Hence, themodel predicts the velocity component in both directions andthen could be developed in 3D time-series data. The used datain this work, have been recorded during an empirical strainingturbulence deformation in 0.4 s.B. GRU modelThe proposed GPU model is created with data series involv-ing two velocity components in x and y directions and two-position coordinates x and y. Every fluid particle at a specifiedtime has a velocity component, and based on the Lagrangianview; they are dependent on the time and position. Bothposition vectors also function of time and primary position.The input features are on different scales, and then it isessential to scale the features. A function is defined to createtime-series data set. The data are split into 80% training and20% test data set. The GRU model is created with one GRUlayer and one Dense layer, and the model is optimized withan Adam optimizer. In order to evaluate the model, the meanabsolute error (MAE) and coefficient of determination (R2)are measured.IV. RESULTThe explained method in the study is based on the capabilityof DL via GRU, which is able to store long-term dependencies.Fig. 2 represents the result of this model that has been usedto predict the velocity components in the y-direction. In Fig.Fig. 2, the actual data, hidden and covered by train dataand predicted data, dictates the suggested model could makeremarkable forecasting for a future time.Fig. 2. GRU model for turbulence flow velocity in y direction with spatialtemporal featuresFor the conducted model, MAE and R2 were measuredequal to 0.002 and 0.98, respectively. These measurementsdetermine that the GRU model can establish a significantprediction for time series with features that have relationshipsanalogous to described data in this work that could be seen inmany turbulence flow applications.V. CONCLUSIONThis work aimed to determine a method to use spatial-temporal features of the Lagrangian framework data in aturbulent flow to create a prediction model based on DLauthority. In this view, the velocity functions of the positionand time. On the other hand, the position is related to thetime and primary place. DL networks for sequential data havebeen developed in subsets in RNNs such as LSTM and GRU.Turbulence flow is a high dimensional phenomenon, and touse a feature for LSTM/GRU model, it is essential to figureout the main features among the high-dimensional data. Thisstudy proposed a GRU model relying on velocity componentsand the position of the fluid particles and exclusive of highdimensionality. Moreover, GRU can predict a time series withlong-term dependencies based on the result presented and theLagrangian definition for the velocity field, storing long-termdependencies is a crucial factor that led to this significantprediction and matched the actual data in the test. On theother hand, this method creates predictions for every velocitycomponent individually, making it applicable for 2D and 3Dfluid flow. The error measurement represented in the evaluationof this method implies the capability of GRU in this kind ofapplication and could be developed for long-term forecastingstudies.ACKNOWLEDGMENTWe thank Prof. Ármann Gylfason from Reykjavik Univer-sity for his technical comments on the experiment conducted atthe Laboratory of Fundamental Turbulence Research (LFTR)at Reykjavik University. We also acknowledge Prof. Chung-Min Lee from California State University Long Beach for herassistance.REFERENCES[1] S. B. Pope, Turbulent Flows. Cambridge University Press, 2000.[2] P. A. Davidson, Turbulence: An Introduction for Scientists and Engi-neers. Oxford University Press, 2004.[3] F. Toschi and E. Bodenschatz, “Lagrangian properties of particles inturbulence,” Annual Review of Fluid Mechanics, vol. 41, no. 1, pp. 375–404, 2009.[4] G. Yeoh, J. J. Chen, and C. H. Chen, “Investigation of swirling flowsin mixing chambers,” Modelling and Simulation in Engineering, 2011.[5] C.-M. Lee, A. Gylfason, P. Perlekar, and F. Toschi, “Inertial particleacceleration in strained turbulence,” Journal of Fluid Mechanics, vol.785, p. 31–53, 2015.[6] P. A. Srinivasan, L. Guastoni, H. Azizpour, P. Schlatter, and R. Vinuesa,“Predictions of turbulent shear flows using deep neural networks,” Phys.Rev. Fluids, vol. 4, p. 054603, May 2019.[7] H. Eivazi, H. Veisi, M. H. Naderi, and V. Esfahanian, “Deep neuralnetworks for nonlinear model order reduction of unsteady flows,”Physics of Fluids, vol. 32, no. 10, p. 105104, 2020.[8] S. Hochreiter and J. Schmidhuber, “Long Short-Term Memory,” NeuralComputation, vol. 9, no. 8, pp. 1735–1780, 11 1997.[9] C. Gu and H. Li, “Review on deep learning research and applicationsin wind and wave energy,” Energies, vol. 15, no. 4, p. 1510, Feb 2022.[10] Y. Wang, R. Zou, F. Liu, L. Zhang, and Q. Liu, “A review of windspeed and wind power forecasting with deep neural networks,” AppliedEnergy, vol. 304, p. 117766, 2021.[11] K. Nam, S. Hwangbo, and C. Yoo, “A deep learning-based forecastingmodel for renewable energy scenarios to guide sustainable energy policy:A case study of korea,” Renewable and Sustainable Energy Reviews, vol.122, p. 109725, 2020.[12] T. Kuremoto, S. Kimura, K. Kobayashi, and M. Obayashi, “Timeseries forecasting using a deep belief network with restricted boltzmannmachines,” Neurocomputing, vol. 137, pp. 47–56, 2014, advanced Intel-ligent Computing Theories and Methodologies.[13] J. L. Lumley, “The structure of inhomogeneous turbulent flows,” Atmo-spheric Turbulence and Radio Wave Propogation, pp. 166–178, 1967,nauka, Russia.[14] J. L, Lumley, Stochastic tools in turbulence. Elsevier, 1970.[15] SCHMID and P. J., “Dynamic mode decomposition of numerical andexperimental data,” Journal of Fluid Mechanics, vol. 656, p. 5–28, 2010.[16] Y. Cengel and J. Cimbala, Fluid Mechanics Fundamentals and Appli-cations. McGraw Hill, 2017.[17] K. Cho, B. van Merriënboer, D. Bahdanau, and Y. Bengio, “On theproperties of neural machine translation: Encoder–decoder approaches,”in Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics andStructure in Statistical Translation. Doha, Qatar: Association forComputational Linguistics, Oct. 2014, pp. 103–111.[18] J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation ofgated recurrent neural networks on sequence modeling,” in NIPS 2014Workshop on Deep Learning, December 2014, 2014.

The capability of recurrent neural networks to predict turbulence flow via spatiotemporal features

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The capability of recurrent neural networks to predict turbulence flow via spatiotemporal features

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