Neural ensemble Kalman filter: Data assimilation for compressible flows with shocks

TL;DR

This paper introduces the neural EnKF, a novel data assimilation method that embeds neural networks within the ensemble Kalman filter to effectively handle shocks in compressible flows, avoiding nonphysical artifacts.

Contribution

The paper proposes a neural network-based extension of the EnKF that uses physics-informed transfer learning to improve data assimilation near shocks in compressible flows.

Findings

Neural EnKF avoids spurious oscillations near shocks.

It effectively models sharp flow features with neural network parameter ensembles.

Demonstrated success on Burgers' equation, shock tube, and blast wave simulations.

Abstract

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We show that the poor performance of the standard EnKF may be attributed to the bimodal forecast distribution that can arise in the vicinity of an uncertain shock location; this violates the assumptions underpinning the EnKF, which assume a forecast which is close to Gaussian. To address this issue we introduce the new neural EnKF. The basic idea is to systematically embed neural function approximations within ensemble DA by mapping the forecast ensemble of shocked flows to the parameter space (weights and biases) of a deep neural network (NN) and to subsequently perform DA in that space. The nonlinear mapping encodes sharp and smooth flow features in an ensemble of NN parameters. Neural EnKF updates are therefore well-behaved only if the NN parameters vary smoothly within the neural representation of the forecast ensemble. We show that such a smooth variation of network parameters can be enforced via physics-informed transfer learning, and demonstrate that in so-doing the neural EnKF avoids the spurious oscillations and nonphysical features that plague the standard EnKF. The applicability of the neural EnKF is demonstrated through a series of systematic numerical experiments with an inviscid Burgers' equation, Sod's shock tube, and a two-dimensional blast wave.