PaperlayerView exact revision on arXiv

Source-linked AI summary

Synthetic turbulent inflow generator using machine learning

Kai Fukami, Yusuke Nabae, Ken Kawai, Koji Fukagata

arXiv:1806.08903v3physics.flu-dyn

TL;DR

The paper seeks a machine-learned alternative to conventional driver simulations or synthetic turbulent inflow generators. An autoencoder-type CNN combined with an MLP is trained on instantaneous velocity fields to predict cross-sectional fields at specified future times. The MLTG accurately reproduces turbulence statistics and spatio-temporal development of cross-sectional structure, and maintains turbulent channel flow up to 10 000 wall unit time at much lower computational cost than the conventional driver.

  • Problem

    The paper seeks a machine-learned alternative to conventional driver simulations or synthetic turbulent inflow generators.

    Source: §I · p. 4

  • Method

    An autoencoder-type CNN combined with an MLP is trained on instantaneous velocity fields to predict cross-sectional fields at specified future times.

    Source: §IV · p. 22

  • Results

    The MLTG accurately reproduces turbulence statistics and spatio-temporal development of cross-sectional structure, and maintains turbulent channel flow up to 10 000 wall unit time at much lower computational cost than the conventional driver.

    Source: §IV · p. 22

  • Takeaways & Limitations

    The MLTG provides time-dependent inflow for inflow-outflow DNS and can support long runs sufficient to accumulate turbulent statistics.

    Source: §IV · p. 22

Abstract

from arXiv · show

We propose a methodology for generating time-dependent turbulent inflow data with the aid of machine learning (ML), which has a possibility to replace conventional driver simulations or synthetic turbulent inflow generators. As for the ML model, we use an auto-encoder type convolutional neural network (CNN) with a multi-layer perceptron (MLP). For the test case, we study a fully-developed turbulent channel flow at the friction Reynolds number of ${\rm Re}_{\tau} = 180$ for easiness of assessment. The ML models are trained using a time series of instantaneous velocity fields in a single cross-section obtained by direct numerical simulation (DNS) so as to output the cross-sectional velocity field at a specified future time instant. From the a priori test in which the output from the trained ML model are recycled to the input, the spatio-temporal evolution of cross-sectional structure is found to be reasonably well reproduced by the proposed method. The turbulence statistics obtained in the a priori test are also, in general, in reasonable agreement with the DNS data, although some deviation in the flow rate was found. It is also found that the present machine-learned inflow generator is free from the spurious periodicity, unlike the conventional driver DNS in a periodic domain. As an a posteriori test, we perform DNS of inflow-outflow turbulent channel flow with the trained ML model used as a machine-learned turbulent inflow generator (MLTG) at the inlet. It is shown that the present MLTG can maintain the turbulent channel flow for a long time period sufficient to accumulate turbulent statistics, with much lower computational cost than the corresponding driver simulation. It is also demonstrated that we can obtain accurate turbulent statistics by properly correcting the deviation in the flow rate.

I. INTRODUCTION

The introduction motivates machine-learned turbulent inflow as an alternative to conventional generators, especially periodic driver simulations, and outlines a CNN–MLP approach for predicting future cross-sectional flow fields.

I. INTRODUCTION

  • Driver simulations add computational cost and can produce spurious periodicity from streamwise periodicity in their computational domain.The introduction also notes that generated fluctuations need spectral content similar to actual turbulence or they dissipate quickly.Source: §I · p. 2
  • The proposed machine-learned inflow generator combines an autoencoder-type CNN with an MLP to predict future cross-sectional flow fields.The CNN compresses cross-sectional data to extract spatial features, while the MLP regresses their temporal relationship.Source: §I · p. 4
  • The model is trained on DNS cross-sectional data to predict the next-time-step field, then tested recursively and as an inflow condition in inflow-outflow DNS.The a priori test recycles model output as input; the a posteriori test uses the trained generator to provide time-dependent inlet conditions.Source: §I · pp. 4–5

A. Training Procedure

The training data come from DNS of fully developed turbulent channel flow at Re_tau = 180. The model learns to map instantaneous cross-sectional velocity and pressure fluctuations to a later field.

A. Training Procedure

  • DNS time series from a single y–z cross-section provide the training data for the fully developed turbulent channel-flow test case.The channel flow is studied at Re_tau = 180.Source: A. Training Procedure · p. 5
  • The model uses velocity and pressure fluctuations as input and output, minimizing mean squared error against the DNS field at the next time step.The input fluctuations are u′, v′, w′, and p′.Source: A. Training Procedure · p. 6
  • The learned time interval is Δt+ = 1.26, corresponding to 10 DNS time steps.Source: A. Training Procedure · p. 6

B. Machine-learned turbulence generator

The generator compresses cross-sectional fields with convolution layers, regresses temporal relationships in an MLP, and reconstructs the next field. The authors compare model variants and report that Case 1 learns most successfully.

B. Machine-learned turbulence generator

A. A priori test: recycling within machine-learned model

The a priori test recursively feeds the trained model’s output back as input to assess whether it can sustain turbulent cross-sectional evolution without further DNS data. It reproduces key structures and statistics best in Case 1, but mean-flow bias and quantitative discrepancies remain.

A. A priori test: recycling within machine-learned model

  • Case 1 gives reasonable agreement with DNS for all Reynolds-stress components, while Case 2 underestimates statistics, especially for u and w.The text attributes Case 2’s underestimation to overcompression of the latent vector fed to the MLP.Source: A. A priori test: recycling within… · pp. 11–12
  • Cases 3 and 4 produce qualitatively similar statistics, but accuracy is poor for R11 and R33 in Case 3 and R22 in Case 4.Source: A. A priori test: recycling within… · p. 12
  • Mean fluctuation profiles are substantially nonzero because training imposes no zero-mean constraint; the resulting bulk-mean error is 0.5% of the original flow’s bulk-mean velocity.The DNS mean profiles are zero, whereas the model’s are not.Source: A. A priori test: recycling within… · p. 12
  • After correcting the fluctuations, Case 1 agrees reasonably with DNS statistics, whereas Cases 2–4 remain poorer, especially for v and w.The corrected statistics are presented in Figure 6.Source: A. A priori test: recycling within… · p. 13, Figure 6 · p. 14
  • The streamwise-velocity spanwise spectrum agrees reasonably with DNS, but high-wavenumber components attenuate, more strongly in higher-compression Case 2.Source: A. A priori test: recycling within… · p. 13, Figure 7 · p. 15
  • Recycled outputs sustain spatio-temporal evolution similar to DNS, with Case 1 closest among the four tested cases.The test starts from a single DNS snapshot and recycles model outputs as inputs.Source: A. A priori test: recycling within… · pp. 10, 13
  • Unlike periodic-domain driver DNS, the MLTG shows no spurious periodicity corresponding to domain length divided by advection velocity.The authors suggest the model learns a nonlinear relation between consecutive time instants, acting as a surrogate for the time-discretized Navier–Stokes system.Source: A. A priori test: recycling within… · pp. 14, 16
  • Case 1 substantially underestimates the integral time scale, indicating that network structure and parameters need improvement for closer quantitative agreement.Source: A. A priori test: recycling within… · p. 18

B. A posteriori test: inflow-outflow DNS using machine-learned inflow generators

The trained MLTG supplies time-dependent inlet data for an inflow-outflow channel DNS, which is run long enough to accumulate turbulence statistics. The flow recovers downstream, the corrected inflow yields statistics in reasonable agreement with periodic DNS, and generation is substantially faster than a driver simulation.

B. A posteriori test: inflow-outflow DNS using machine-learned inflow generators

  • The inlet data use uncorrected Case 1 or corrected Case 1′ fluctuations, with fields generated every 10 DNS steps and linear interpolation between them.Source: B. A posteriori test: inflow-outflow… · p. 18
  • After slight fluctuation damping near the inlet, the flow recovers correct statistics by x/δ ≃ 2, and the simulation continues to t+ = 10,000 for statistical accumulation.Source: B. A posteriori test: inflow-outflow… · p. 20
  • Corrected Case 1′ produces turbulence statistics in reasonable agreement with periodic DNS, outperforming uncorrected Case 1, whose deviation is attributed to increased flow rate.The result supports using the MLTG in inflow-outflow DNS when it reproduces inflow spatio-temporal characteristics reasonably well.Source: B. A posteriori test: inflow-outflow… · p. 20
  • The amount and kinds of inlet error that still permit correct downstream statistics remain undetermined.Source: B. A posteriori test: inflow-outflow… · p. 20
  • Against the driver DNS run, actual inflow-generation speedups are 1,800 times on CPU and 5,800 times on GPU; the model generates a cross-sectional velocity field every 10 DNS time steps.Source: B. A posteriori test: inflow-outflow… · p. 22

IV. CONCLUSIONS

The study introduces an MLTG based on an autoencoder-type CNN and MLP, trained on DNS cross-sectional velocity fields to predict a future field. Tests at Re_τ = 180 show that it can sustain inflow-outflow channel turbulence for statistics collection at lower computational cost than a conventional driver, while conclusions remain bounded by flow-rate deviations and training-data and model-accuracy constraints.

IV. CONCLUSIONS

  • The MLTG uses an autoencoder-type CNN combined with an MLP to predict future cross-sectional velocity fields from DNS time series.The test case was turbulent channel flow at Re_τ = 180.Source: §IV · p. 22
  • The a priori test found that the MLTG reproduced cross-sectional structure and turbulence statistics, although some flow-rate deviation remained.It was also free from the spurious periodicity associated with conventional driver DNS in a periodic domain.Source: §IV · p. 22
  • For 10,000 wall-unit time, the MLTG maintained turbulent channel flow long enough to accumulate statistics, at much lower computational cost than the conventional driver.The conclusion presents the MLTG as an attractive alternative when many simulations share statistically the same inflow but have different downstream conditions.Source: §IV · pp. 22–23
  • The method could extend to spatially developing boundary layers and flows around bodies, but its accuracy should be assessed for each problem.The conclusion describes these extensions as straightforward, not as already validated.Source: §IV · p. 23
  • A priori results were sensitive to machine-learning choices such as layer and unit counts, motivating broader searches for more accurate network structures.LSTM is suggested as one possible avenue for improving temporal characteristics.Source: §IV · p. 23
  • A major drawback relative to conventional synthetic turbulence generators is the need for target-flow spatio-temporal data to train the network.The authors identify learning from lower-order information, such as spatio-temporal correlations alone, as an ultimate goal.Source: §IV · p. 23

ACKNOWLEGMENTS

The authors thank colleagues for fruitful discussion and acknowledge support from a JSPS KAKENHI grant.

Loading 1806.08903v3…