Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems
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Abstract (arXiv)
Data-driven modeling of nonlinear dynamical systems is often hampered by measurement noise. We propose a denoising framework, called Runge-Kutta and Total Variation Based Implicit Neural Representation (RKTV-INR), that represents the state trajectory with an implicit neural representation (INR) fitted directly to noisy observations. Runge-Kutta integration and total variation are imposed as constraints to ensure that the reconstructed state is a trajectory of a dynamical system that remains close to the original data. The trained INR yields a clean, continuous trajectory and provides accurate first-order derivatives via automatic differentiation. These denoised states and derivatives are then supplied to Sparse Identification of Nonlinear Dynamics (SINDy) to recover the governing equations. Experiments demonstrate effective noise suppression, precise derivative estimation, and reliable system identification.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 22 of its 67 references that are in the map. First posted on arXiv 17 Sep 2025.
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22 of 67 references.
References · 22
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- 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
- 2022A Review of Data-Driven Discovery for Dynamic Systemscited by 18
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