  We present a new data-driven model to reconstruct nonlinear flow from
spatially sparse observations. The 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 the 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 as Semi-Conditional Variational Autoencoder (SCVAE). 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 the Bergen Ocean Model. The reconstruction errors are compared to those of
the Gappy Proper Orthogonal Decomposition (GPOD) method.
