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Main Authors: Yao, Jiaqi, Mitchell, Lewis, Maclean, John, Saratchandran, Hemanth
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.14219
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author Yao, Jiaqi
Mitchell, Lewis
Maclean, John
Saratchandran, Hemanth
author_facet Yao, Jiaqi
Mitchell, Lewis
Maclean, John
Saratchandran, Hemanth
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_14219
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems
Yao, Jiaqi
Mitchell, Lewis
Maclean, John
Saratchandran, Hemanth
Machine Learning
Dynamical Systems
Computational Physics
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.
title Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems
topic Machine Learning
Dynamical Systems
Computational Physics
url https://arxiv.org/abs/2509.14219