Feature-preserving Latent-EnKF for Data Assimilation of Flows with Shocks

2026-06-10

AI Summary

This study addresses the challenge of spurious oscillations in analysis fields produced by traditional ensemble Kalman filters when assimilating compressible flows containing shocks, which arise due to non-Gaussian, multimodal statistics induced by uncertainty in shock location. To overcome this, the authors propose a feature-preserving latent-space ensemble Kalman filter that leverages a deep autoencoder to construct a low-dimensional latent space. Ensemble updates are performed in this latent space to yield smooth manifold representations of both shock structures and flow features, which are then mapped back to physical space via a shared decoder. This approach preserves the sharpness of discontinuities during assimilation without requiring member-specific ordering, positivity constraints, or specialized training. Validated on the Sod shock tube and Mach 2 cylinder-induced shock interaction cases, the method accurately recovers shocks and contact discontinuities while eliminating spurious oscillations.

Abstract

The ensemble Kalman filter (EnKF) is widely adopted for sequential data assimilation, but fails for solutions with discontinuities, such as shocks in compressible flows. Uncertainty in shock location induces multimodal ensemble statistics that violate the Gaussian assumptions underlying the EnKF, producing large-scale spurious oscillations in the analysis state. We introduce a feature-preserving latent-EnKF that performs the ensemble update in a learned low-dimensional latent space, where shock and flow features admit a smooth manifold representation, thereby preserving sharp features during EnKF analysis. The updated latent state is mapped back to physical state through a shared decoder for all ensemble members. The algorithm eliminates the member-specific ordered training and positivity flooring used in prior approaches. Numerical experiments on a Sod shock tube and Mach 2 shock interaction with a 2D cylinder, using sparse and noisy observations, show accurate feature recovery of shocks and contact discontinuities without spurious oscillations.

Problem

• data assimilation
• shocks
• ensemble Kalman filter
• discontinuities
• spurious oscillations

Innovation

• latent-EnKF
• feature-preserving
• data assimilation
• shock capturing
• ensemble Kalman filter