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

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The is version of conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification the prediction. show that in our model, conditioning on measurements complete data leads CVAE where only decoder depends measurements. For this reason we call as Semi-Conditional Variational Autoencoder (SCVAE). method, reconstructions associated estimates are illustrated velocity simulations 2D around cylinder bottom currents Bergen Ocean Model. errors compared those Gappy Proper Orthogonal Decomposition (GPOD) method.