# On the inadequacy of nudging data assimilation algorithms for non-dissipative systems

arXiv: https://arxiv.org/abs/2411.08273 · HTML: https://mlsanity.com/paper/2411.08273/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [BLISSNet: Deep Operator Learning for Fast and Accurate Flow Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2602.24228/) (2026)

## Abstract (arXiv)

In this work, we study the applicability of the Azouani-Olson-Titi (AOT) nudging algorithm for continuous data assimilation to evolutionary dynamical systems that are not dissipative. Specifically, we apply the AOT algorithm to a partially dissipative variant of the Lorenz 1963 system, the Korteweg-de Vries equation (KdV) in 1D, and the 2D incompressible Euler equations. Our analysis reveals that both the Euler and KdV equations lack the finitely many determining modes property, leading to the construction of infinitely many solutions with exactly the same sparse observational data, which data assimilation methods cannot distinguish between. Simultaneously, we numerically verify that the AOT algorithm successfully recovers these counterexamples for the damped and driven KdV equation, which is dissipative. Additionally, to further support our argument, we present numerical evidence showing that the AOT algorithm is ineffective at accurately recovering solutions for a partially dissipative variant of the Lorenz 1963 system.