What is machine learning learning? Autoencoders for reduced-order modelling of turbulence.

  • Magri, Luca (Imperial College London)
  • Kelshaw, Daniel (Imperial College London)
  • Doan, Nguyen Anh Khoa (TU Delft )

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This talk will give provide perspectives about the opportunities and limitations of machine learning in fluids, with a focus on the interpretability of autoencoders for reduced-order modelling of turbulent flows. Autoencoders are function representations that enable a reduced-order representation of data. They con- sist of an encoder, which downsamples the data degrees of freedom into a latent space, and a decoder, which upsamples the latent space back to the physical space. If only linear activations are employed, an autoencoder learns the proper orthogonal modes of the data, which are physically interpretable modes. When nonlinear activations functions are employed, an autoencoder learns a nonlinear reduced-order model of the data in the latent space. The interpretability of the latent space, however, is not fully established in fluid mechanics. In this work, we physically interpret the latent space with simple tools from geometry. The interpretation is employed on fundamental turbulent flows such as the Kolmogorov flow and a channel flow. The results show that the autoencoder learns an optimal submanifold in which the reduced-order dynamics is accurately described (both in space and time). The latent variables are exploited for reducing the model’s complexity whilst keeping optimal accuracy on the spatiotemporal dynamics. This work opens opportunities for extracting physical insight from the latent space and for nonlinear model reduction.