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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Related Experiment Video

Updated: May 7, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

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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
PubMed
Summary

We developed a novel denoising framework (RKSDS-INR) for nonlinear dynamical systems. It effectively suppresses noise, enabling accurate system identification from observational data.

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Last Updated: May 7, 2026

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06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

716

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.