Data assimilation and local-in-time global control of inviscid systems using partially resolved measurements
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1.
University of Southern California
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2.
California Institute of Technology
Abstract
Most data assimilation algorithms have focused on dissipative systems, as the method relies on the existence of a global attractor. In this paper, we extend the framework of continuous data assimilation to inviscid models. As a first step towards this goal, we consider two inviscid systems: the passive scalar transport equation and the Euler equation. The data assimilation algorithm we employ utilizes nudging, a method based on a Newtonian relaxation scheme motivated by feedback control. We consider the two systems in an analytic space with a time-dependent analytic radius. This allows us to extract an artificial dissipative term, which is necessary for the application of data assimilation techniques. We establish exponential decay of the error between the data assimilated solution and the reference solution on a finite time interval [0, T∗) , and estimate the error at the end of the algorithm (as t → T∗).
Copyright and License
© 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Acknowledgement
E.C. was supported in part by the Department of Defense Vannevar Bush Faculty Fellowship , under ONR award N00014-22-1-2790.
Conflict of Interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Elizabeth Carlson reports financial support was provided by Office of Naval Research. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data Availability
No data was used for the research described in the article.
Additional details
Funding
- United States Department of Defense
- Vannevar Bush Faculty Fellowship -
- Office of Naval Research
- N00014-22-1-2790
Dates
- Accepted
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2025-09-01
- Available
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2025-09-18Available online
- Available
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2025-09-19Version of record