Learning extrapolation in the reconstruction and forecasting of a turbulent velocity flow field using Autoencoders and Singular Value Decomposition

  • Abadía-Heredia, Rodrigo (Universidad Politécnica de Madrid)
  • Crialesi-Esposito, Marco (Istituto Nazionale di Fisica Nucleare)
  • Lopez-Martin, Manuel (Universidad Politécnica de Madrid)
  • Brandt, Luca (KTH Royal Institute of Technology)
  • Le Clainche, Soledad (Universidad Politécnica de Madrid)

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Singular Value Decomposition (SVD) [1] is a well-known mode-decomposition method aimed at decomposing a spatio-temporal data set in its dominant flow features, i.e., modes. In this paper we explore the learning extrapolation capability of a Deep Learning (DL) architecture, known as Autoencoder, which is similar to SVD in the sense that it is also capable of compressing and reconstructing a dataset. The main differences between these two models are that, on the one hand, the autoencoders are stochastic, use linear or non-linear functions and need to be trained, and on the other hand, the SVD is deterministic and uses linear functions. This work is focused on comparing the performance of both models either for reconstruction and forecasting tasks. In this meaning, we explore two different architectures of Autoencoders: conv-Autoencoder and dense-Autoencoder. Where the first one is composed by Convolutional layers [2] and the second one by Dense layers. The database we use in this work, to test and compare the performance of both autoencoders and SVD, corresponds to the streamwise velocity of a turbulent flow [3]. We finally show that both Autoencoders (dense and convolutional) can reconstruct the entire data set by training it only with half of the data, in contrast to SVD that requires the whole data set. Also, we show the strength of using convolutional layers to capture some spatial patterns inside the turbulent flow and use them to perform a future prediction, in contrast to both SVD and the dense Autoencoder.