Feature preserving data assimilation via feature alignment
Amit N. Subrahmanya, Adrian Sandu
TL;DR
This paper tackles data assimilation for systems that develop sharp features like shocks, where traditional ensemble methods smear structures. It introduces a feature-preserving ensemble transform particle filter that uses feature extraction from density fields, dynamic time warping for feature alignment, and aligned two-way convex combinations to transport particles while preserving features. The method is demonstrated on compressible Euler problems in 1D and 2D (Sod, Toro, Shu-Osher, and a blast-wave case), showing improved qualitative preservation of shocks and discontinuities with comparable quantitative error to standard ETPF. The work highlights the importance of feature-aware transport in high-dimensional DA and discusses computational costs, limitations, and avenues for future multi-dimensional alignment improvements. Overall, the approach offers a principled way to maintain physically meaningful structures during assimilation in shock-dominated flows, potentially benefiting predictive capabilities in aerodynamics and related fields.
Abstract
Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that exhibit the formation of structures, called features, which have to be accurately captured by the assimilation framework. For example, fluids can develop features such as shockwaves and contact discontinuities that need to be tracked and preserved during data assimilation. State-of-the-art data assimilation techniques are agnostic of such features. Current ensemble-based methods construct state estimates by taking linear combinations of multiple ensemble states; repeated averaging tends to smear the features over multiple assimilation cycles, leading to nonphysical state estimates. A novel feature-preserving data assimilation methodology that combines sequence alignment with the ensemble transform particle filter is proposed to overcome this limitation of existing assimilation algorithms. Specifically, optimal transport of particles is performed along feature-aligned characteristics. The strength of the proposed feature-preserving filtering approach is demonstrated on multiple test problems described by the compressible Euler equations.