Semi-conditional variational auto-encoder for flow reconstruction and uncertainty quantification from limited observations

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  • Kristian Gundersen
    Department of Mathematics, University of Bergen 1 , 5020 Bergen, Norway
  • Anna Oleynik
    Department of Mathematics, University of Bergen 1 , 5020 Bergen, Norway
  • Nello Blaser
    Department of Informatics, University of Bergen 2 , 5020 Bergen, Norway
  • Guttorm Alendal
    Department of Mathematics, University of Bergen 1 , 5020 Bergen, Norway

Description

<jats:p>We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The proposed model is a version of a Conditional Variational Auto-Encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason, we call the model semi-conditional variational autoencoder. The method, reconstructions, and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from a simulation of the southern North Sea by the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy proper orthogonal decomposition method.</jats:p>

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