New method enhances equation discovery from noisy data using Koopman dynamics

Researchers have developed a dynamics-aware method for identifying governing equations from sparse and noisy data, building upon techniques like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE Functional Identification (PDE-FIND). The new approach utilizes Koopman-based upsampling methods, including Dynamic Mode Decomposition (DMD) and its variants, to interpolate and denoise data before derivative estimation and sparse regression. This preprocessing step aims to improve the accuracy of derivative estimation, which is often unreliable with sparse and noisy measurements. The method was tested on several ODE and PDE systems, showing that Koopman-based upsampling, particularly Polynomial EDMD for ODEs, offers performance gains over traditional interpolation techniques. AI

IMPACT Enhances the ability to discover underlying physical laws from experimental data, potentially accelerating scientific research.

RANK_REASON The cluster contains a research paper detailing a new methodology for scientific discovery. [lever_c_demoted from research: ic=1 ai=1.0]

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• Burgers
• Dynamic Mode Decomposition
• Koopman
• Lorenz-63
• PDE functional identification
• Pongpisit Thanasutives
• Van der Pol

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