Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems
This work addresses noise issues in dynamical system modeling for researchers in applied mathematics and engineering, representing an incremental improvement by integrating existing methods like SINDy with a novel denoising approach.
The paper tackles the problem of measurement noise in data-driven modeling of nonlinear dynamical systems by proposing RKTV-INR, a denoising framework that uses implicit neural representations with Runge-Kutta and total variation constraints, resulting in effective noise suppression and reliable system identification as demonstrated in experiments.
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.