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 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.