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[2511.17772] Weighted Birkhoff Averages Accelerate Data-Driven Methods
Summary
The paper discusses Weighted Birkhoff Averages, a method that accelerates convergence in data-driven algorithms for dynamical systems, demonstrating improved performance across various applications.
Why It Matters
This research is significant as it addresses the slow convergence of traditional ergodic averages in data-driven methods, offering a simple yet effective solution that can enhance the efficiency of algorithms used in fields like fluid dynamics and climate modeling.
Key Takeaways
- Weighted Birkhoff averages can significantly speed up convergence rates in data-driven algorithms.
- The method is easy to implement and integrates well with existing techniques.
- Demonstrated effectiveness across diverse applications, including fluid flows and climate data.
- Weighting the data incurs no additional costs while enhancing results.
- Potential for broader implications in various scientific and engineering fields.
Mathematics > Dynamical Systems arXiv:2511.17772 (math) [Submitted on 21 Nov 2025 (v1), last revised 18 Feb 2026 (this version, v2)] Title:Weighted Birkhoff Averages Accelerate Data-Driven Methods Authors:Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook View a PDF of the paper titled Weighted Birkhoff Averages Accelerate Data-Driven Methods, by Maria Bou-Sakr-El-Tayar and 2 other authors View PDF HTML (experimental) Abstract:Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even exponentially) and can be incorporated seamlessly into existing methods. We demonstrate this with five weighted algorithms: weighted Dynamic Mode Decomposition (wtDMD), weighted Extended DMD (wtEDMD), weighted Sparse Identification of Nonlinear Dynamics (wtSINDy), weighted spectral measure estimation, and weighted diffusion forecasting. Across examples ranging from fluid flows to El Niño data, the message is clear: weighting costs nothing, is easy to implement, and often delivers markedly better results from the same data. Subjects: Dynamical Systems (math.DS); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2511.17772 [math.DS] (or arXiv:2511.17772v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2511.17772 Focus to learn more arXiv-issued DOI via DataCite Submissi...