Feature-Informed Data Assimilation -- Definitions and Illustrative Examples

TL;DR

This paper introduces feature-informed data assimilation (FIDA), a novel approach that incorporates feature events like shock waves and wavefronts into state estimation, using a set-valued observation operator, demonstrated through three examples.

Contribution

The paper formulates FIDA with a set-valued observation operator, expanding data assimilation techniques to include feature events in dynamical systems.

Findings

FIDA effectively incorporates feature events into data assimilation.

The approach is demonstrated in three diverse scientific and engineering applications.

FIDA's set-valued operator differs fundamentally from traditional observation models.

Abstract

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the estimation of state variables and unknown parameters. The observation operator in FIDA is a set-valued functional, which is fundamentally different from the observation operators in conventional data assimilation. Demonstrated in three example, FIDA problems introduced in this note exist in a wide spectrum of applications in science and engineering.