In order to effectively reduce the design cost and cycle time of using CFD methods, the reduced-order model (ROM) has gained wide attention in recent years. For complex compressible flows, using linear methods such as Proper Orthogonal Decomposition (POD) for flow field dimensionality reduction requires a large number of modes to ensure the reconstruction accuracy. It has been shown that the modes number can be effectively reduced by using nonlinear dimensionality reduction methods. Convolutional Autoencoder (CAE) is a kind of neural network composed of encoder and decoder, which can realize data dimensionality reduction and recon-struction, and can be regarded as a nonlinear extension of POD method. CAE is used for nonlinear dimension-ality reduction, and Transformer is used for time evolution. The CAE-Transformer can obtain high reconstruction and prediction accuracy on the premise of using less latents for unsteady compressible flows.
The basic framework of CAE-Transformer is mainly based on paper . It consists of CAE and Transformer, where the encoder in CAE reduces the dimensionality of the time series flow field to achieve feature extraction, Transformer learns low dimensional spatiotemporal features and makes predictions, and the decoder in CAE realizes flow field reconstruction.
- Input：Input the flow field for a period of time
- Compression：Extract high-dimensional spatiotemporal flow characteristics by dimensionality reduction of the flow field using the encoder of CAE
- Evolution：Learning the evolution of spatiotemporal characteristics of low dimensional spatial flow fields through Transformer and predicting the next moment
- Reconstruction：Restore the predicted low-dimensional features of the flow field to high-dimensional space through the decoder of CAE
- Output：Output the predicted results of the transient flow field at the next moment
The CAE-Transformer model actually adopts the Informer model, which is based on the Transformer architecture, to achieve long-term sequence prediction. The basic framework of Informer is primarily based on the paper
- Input Encoding: Converts long-term sequence data into vector representations
- Encoder: Utilizes the ProbSpare Self-Attention mechanism and feed-forward neural networks to encode the vector sequence. It employs Self-attention Distilling to privilege advantageous features, reducing spatial complexity, and efficiently extracting features
- Encoder Stacking: Stacks multiple self-attention encoders to extract higher-level features
- Decoder: Converts the output of the encoder into target predictions
- Output Decoding: Maps the decoder output back to the original target prediction space
Source: Numerical simulation flow field data of Tow-dimensional Kelvin-Helmholtz instability problem, provided by Professor Yu Jian from the School of Aeronautic Science and Engineering, Beihang University.
Establishment method: The calculation status and establishment method of the dataset can be found in paper
Data description: The coordinate range is [-0.5, 0.5], and the calculation time t ranges from [0, 1.5] and is divided into an average of 1786 time steps. A total of 1786 flow field snapshots, each with a matrix size of (256, 256).
The download address for the dataset is: data_driven/cae-lstm/kh/dataset
The model is trained by single machine and single card. According to the training task requirements, run cae_train.py and tansformer_train.py to start training; Before training, relevant training conditions need to be set in config.yaml.
- Train the CAE network:
python -u cae_train.py --mode GRAPH --save_graphs_path ./graphs --device_target GPU --device_id 0 --config_file_path ./config.yaml
- Train the Transformer network:
python -u transformer_train.py --mode GRAPH --save_graphs_path ./graphs --device_target GPU --device_id 0 --config_file_path ./config.yaml
Run the prediction.py for post-processing operation, this operation will predict the dimensionality reduction and reconstruction data of CAE, the evolution data of Transformer, and the flow field data predicted by CAE-Transformer based on the weight parameter file of the training results. This operation also calculates the average relative error of CAE reconstruction data and CAE-Transformer predicted flow field data, respectively.
The default output path for the above post-processing is ./prediction_result, the save path can be modified in config.yaml.
The following are the actual flow field, CAE-Transformer prediction results, and prediction errors.
The first two flow field results show the variation of density at different positions in the flow field over time, while the third error curve shows the variation of the average relative error between the CAE reconstructed flow field and the CAE-Transformer flow field and the real flow field label over time. The error of CAE-Transformer prediction results is greater than that of CAE reconstruction because the former has more Transformer evolution error than the latter, but the overall prediction time error remains below 0.02, meeting the accuracy requirements of flow field prediction.
