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

Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations