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[2511.18555] A joint optimization approach to identifying sparse dynamics using least squares kernel collocation
Summary
The paper presents a novel modeling framework for learning ordinary differential equations (ODEs) from limited and noisy data, enhancing accuracy and robustness in dynamic system identification.
Why It Matters
This research is significant as it addresses the challenge of accurately modeling dynamic systems from sparse data, which is crucial in fields like engineering, physics, and data science. The proposed methodology improves upon existing algorithms, offering better performance in real-world applications where data is often incomplete or noisy.
Key Takeaways
- Introduces an all-at-once modeling framework for ODEs.
- Combines sparse recovery strategies with RKHS techniques.
- Demonstrates improved accuracy and robustness to noise.
- Extends the modeling flexibility of existing equation discovery methods.
- Applicable in various fields requiring dynamic system analysis.
Statistics > Methodology arXiv:2511.18555 (stat) [Submitted on 23 Nov 2025 (v1), last revised 20 Feb 2026 (this version, v2)] Title:A joint optimization approach to identifying sparse dynamics using least squares kernel collocation Authors:Alexander W. Hsu, Ike Griss Salas, Jacob M. Stevens-Haas, J. Nathan Kutz, Aleksandr Aravkin, Bamdad Hosseini View a PDF of the paper titled A joint optimization approach to identifying sparse dynamics using least squares kernel collocation, by Alexander W. Hsu and 5 other authors View PDF HTML (experimental) Abstract:We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE. Our numerical experiments reveal that the proposed strategy leads to significant gains in terms of accuracy, sample efficiency, and robustness to noise, both in terms of learning the equation and estimating the unknown states. This work demonstrates capabilities well beyond existing and widely used algorithms while extending the modeling flexibility of other recent developments in equation discovery. Subjects: Methodology (stat.ME); Machine Learning (cs.LG); Dynamical Systems (math.DS); Machine Learning (stat.ML) Cite as:...
