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

TL;DR

This paper introduces a Semi-Conditional Variational Autoencoder (SCVAE) for reconstructing nonlinear flow fields from sparse data, providing probabilistic predictions and uncertainty quantification, demonstrated on fluid flow simulations.

Contribution

The paper proposes a novel SCVAE model where only the decoder depends on measurements, improving flow reconstruction and uncertainty quantification from limited observations.

Findings

SCVAE outperforms GPOD in flow reconstruction accuracy

Provides probabilistic uncertainty estimates for flow predictions

Effective on 2D flow around a cylinder and ocean current data

Abstract

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.