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A new prediction method of unsteady wake flow by the hybrid deep neural network
Renkun Han, Yixing Wang, Yang Zhang, Gang Chen
TL;DR
Fast and accurate prediction of unsteady flows is difficult because their dynamics are high-dimensional and nonlinear. The paper designs a hybrid CNN–ConvLSTM–DeCNN architecture that captures spatio-temporal features directly from high-dimensional flow fields and tests future-field prediction. Across cylinder and airfoil cases, the predicted fields agree well with CFD results.
Problem
Fast and accurate prediction of unsteady flow is challenging because the flow fields are high-dimensional and nonlinear.
Method
A hybrid deep neural network combines CNN, ConvLSTM, and DeCNN components to capture spatio-temporal features directly from high-dimensional flow fields.
Results
The trained hybrid deep neural networks predict future flow fields that agree well with flow fields calculated by the CFD solver.
Takeaways & Limitations
The hybrid network achieves fast and accurate prediction of unsteady flow fields for the tested cylinder and airfoil cases.
Takeaways & Limitations
Reduced-order approaches discussed in the paper are limited by linear or weakly nonlinear assumptions, restricting the flow fields they can analyze properly.
Abstract
from arXiv · showhide
The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the unsteady flow spatio-temporal features directly from the high-dimensional unsteady flow fields. The hybrid deep neural network is constituted by the convolutional neural network (CNN), convolutional Long Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). The flow around a cylinder at various Reynolds numbers and the flow around an airfoil at higher Reynolds number are carried out to establish the datasets used to train the networks separately. The trained hybrid DNNs were then tested by the prediction of the flow fields at future occasions. The predicted flow fields using the trained hybrid DNNs are in good agreement with the flow fields calculated directly by the computational fluid dynamic solver.
1. Introduction
The paper addresses the difficulty of fast, accurate prediction of high-dimensional, nonlinear unsteady flows. It proposes a hybrid deep neural network to reduce dimensionality and capture spatio-temporal dynamics directly from flow fields for future prediction.
- Prior limitations: Reduced-order methods such as POD and DMD improve efficiency but often rely on linear or weakly nonlinear assumptions that limit the flow fields they can analyze.These methods can simulate physical and dynamic systems with increased computational efficiency while maintaining reasonable accuracy.
- Motivation: High-fidelity unsteady-flow modeling is challenging because nonlinear coupled physics generate complex spatial-temporal dynamics and require fast, accurate prediction.The need is especially acute for flows involving fluid-structure interactions and for applications requiring low computational cost.
- Prior limitations: Earlier deep-learning approaches mainly reduced dimensionality or reconstructed the current flow field, rather than modeling spatio-temporal dynamics and predicting future fields.This limitation motivates a method that learns temporal evolution instead of only representing instantaneous states.
- Proposed approach: The proposed hybrid network combines dimensionality reduction with learning of the governing system’s attractor to model unsteady-flow spatio-temporal dynamics at low computational cost.The approach is designed to capture more nonlinear feature mappings without an explicit intermediate dimensionality-reduction method.
- Proposed approach: A single neural network is presented to reduce unsteady-flow dimensionality and capture spatio-temporal flow dynamics simultaneously.The paper describes this as different from previous work and applies the mapping directly from high-dimensional flow fields to future occasions.
2. The architecture of the hybrid deep neural network
The hybrid architecture combines CNN, ConvLSTM, and DeCNN layers to learn spatial-temporal features from high-dimensional unsteady flow fields and predict future fields.
- Overall architecture: The hybrid network combines CNN, ConvLSTM, and DeCNN layers to capture accurate spatial-temporal features of unsteady flows.CNN layers extract low-dimensional features, ConvLSTM models temporal behavior, and DeCNN layers reconstruct high-dimensional flow fields.
- CNN layers: CNN layers extract complex features from high-dimensional input fields and represent them in low-dimensional form.The CNN comprises six convolutional layers and produces feature maps for each time-step flow field.
- ConvLSTM layer: ConvLSTM layers capture temporal features between low-dimensional representations and predict future flow-field feature maps.The layer uses feature maps from previous occasions while retaining two-dimensional spatial information.
- DeCNN layers: DeCNN layers reverse the CNN architecture to transform predicted low-dimensional features into high-dimensional output fields matching the input-field dimensions.Deconvolution can restore the output size but cannot restore the matrix before convolution.
- ConvLSTM layer: ConvLSTM retains spatial correlations that traditional LSTMs lose when two-dimensional inputs are resized to one-dimensional vectors.The dimensionality loss in traditional LSTMs can lead to increased prediction errors.
3. Training Method of the Hybrid Deep Neural Network
The training method converts simulated unsteady flow fields into chronological image-like datasets, then trains the network to minimize prediction error against numerical simulations.
- Training data: Chronologically arranged fields from previous occasions form image-like inputs for predicting flow fields at future occasions.The evenly distributed grid points provide pixel-like data for image-to-image regression.
- Data preparation: High-precision numerical simulations generate dynamic unsteady flow-field data recorded at each moment for network training and testing.The original flow quantities are nondimensionalized before dataset construction.
- Data preparation: Each instantaneous field is represented on a uniform Nx × Ny grid with three variables: p*, u*, and v*.Values inside the body are set to 0, and the resulting Nx × Ny × 3 data are arranged chronologically.
- Objective function: RMSE evaluates model performance by comparing network predictions with numerical simulations over the full mesh.The loss uses predictions and numerical simulations at time level t across N mesh nodes.
- Optimization: Adam optimization and backpropagation train the network by minimizing the loss function and updating its learnable kernel parameters.Training is implemented with TensorFlow, using exponential moving averages of gradients and squared gradients in Adam.
4. Results and Discussions
The hybrid deep neural network was trained and tested on cylinder and airfoil flows spanning laminar and turbulent regimes. Its recursive predictions agreed well with CFD fields and captured both spatial structure and temporal evolution, including long-horizon predictions.
- Prediction procedure: The trained network recursively recycled its output as the next input, enabling future flow-field prediction without CFD data for the latter period.The initial input consisted of k CFD snapshots, after which predictions were advanced continuously through time.
- Cylinder results: Predicted cylinder flow fields agreed well with CFD after both a single time-step and 64 time-steps, with no obvious increase in error as recursive steps increased.The comparison covered pressure, streamwise velocity, and vertical velocity for the tested cylinder cases.
- Airfoil and temporal results: The network accurately predicted spatial and temporal evolution for turbulent flow over the airfoil, while predicted time series at selected wake positions agreed very well with CFD.The results supported prediction of both overall flow structures and flow-field evolution across laminar and turbulent cases.
5. Conclusions
The study develops a hybrid deep neural network that captures spatio-temporal features directly from high-dimensional unsteady flow fields and predicts future fields. Across cylinder and airfoil cases, predictions agree well with CFD results, with potential applications where fast high-dimensional flow calculation is needed.
- Network architecture: The method captures spatial-temporal information directly from unsteady flow-field series without relying on separate dimensionality-reduction and temporal-modeling procedures.The architecture is designed to reduce dimensionality and capture spatio-temporal flow features within one neural network.
- Implications: The approach is positioned for fluid-structure interactions and flow control requiring fast, high-dimensional nonlinear unsteady-flow calculations.The study describes the method as a potential reduced-order model for fast unsteady-flow prediction.
- Network architecture: The hybrid network combines CNN, ConvLSTM, and DeCNN layers to encode high-dimensional flow fields, model temporal features, and reconstruct future fields.CNN layers form low-dimensional representations, ConvLSTM predicts future representations, and DeCNN restores the original field dimension.
- Evaluation: Cylinder cases at various Reynolds numbers and higher-Reynolds-number airfoil cases supplied separate training and testing datasets for future-flow prediction.The trained networks were evaluated on predicted flow fields, instantaneous fields, and velocity time histories.
- Evaluation: Predicted flow fields and velocity histories agree well with CFD simulation results across all tested cases.The reported agreement covers both instantaneous flow fields and velocity time histories.
- Evaluation: Differences in object shape and Reynolds number have little effect on prediction accuracy when flow inputs and outputs are treated as images.The authors attribute this behavior to CNN layers capturing characteristics of different flow-field images.
- Limitations and future work: A remaining scope boundary is that future work aims to learn flows across different Reynolds numbers and body shapes simultaneously and predict cases excluded from training.Application to fluid-structure interactions and flow control is also identified for further study.