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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Data denoising and derivative estimation for data-driven modeling of nonlinear dynamical systems
Jiaqi Yao1, Lewis Mitchell1, John Maclean1
1Adelaide Data Science Centre, School of Mathematical Sciences, Adelaide University, Adelaide 5005, South Australia, Australia.
Chaos (Woodbury, N.Y.)
|May 6, 2026
Summary
We developed a novel denoising framework (RKSDS-INR) for nonlinear dynamical systems. It effectively suppresses noise, enabling accurate system identification from observational data.
Area of Science:
- Dynamical Systems and Control
- Machine Learning
- Scientific Computing
Background:
- Data-driven modeling of nonlinear dynamical systems is challenged by measurement noise.
- Accurate state derivatives are crucial for system identification but difficult to obtain from noisy data.
Purpose of the Study:
- To introduce a robust framework for denoising observational data in nonlinear dynamical systems.
- To enable precise estimation of state derivatives for reliable system identification.
Main Methods:
- Proposed RKSDS-INR (Runge-Kutta and Second-Order Derivative Smoothness Based Implicit Neural Representation) framework.
- Utilized Implicit Neural Representations (INRs) fitted to noisy observations.
- Incorporated Runge-Kutta integration and second-order derivative smoothness as constraints.
Main Results:
- Achieved effective noise suppression in state trajectories.
- Demonstrated accurate estimation of first-order derivatives via automatic differentiation.
- Showcased reliable recovery of governing equations using sparse identification.
Conclusions:
- RKSDS-INR framework successfully denoises observational data for dynamical systems.
- The method enables accurate derivative estimation essential for system identification.
- This approach enhances the reliability of data-driven modeling for nonlinear dynamics.
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