Feature-preserving Latent-EnKF for Data Assimilation of Flows with Shocks
For data assimilation in compressible flows with discontinuities, this method overcomes limitations of standard EnKF by preserving sharp features, addressing a known bottleneck in sequential data assimilation.
The paper introduces a feature-preserving latent-EnKF that performs ensemble updates in a learned latent space to handle shocks in compressible flows, eliminating spurious oscillations and accurately recovering shock features with sparse, noisy observations.
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.