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  • Open Access

Moment-based approach to cyclostationary nonlinear inverse modeling under persistent noise forcing

Justin Lien*

Hiroyasu Ando

Yong-Yub Kim

Ingo Richter†

  • *Contact author: lien.justin.t8@dc.tohoku.ac.jp
  • †Present address: Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan.
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Phys. Rev. Research 8, 023178 – Published 18 May, 2026

DOI: https://doi.org/10.1103/j3l8-6j37

Abstract

This study extends the moment-based nonlinear inverse modeling (nLIM) framework from the stationary to the cyclostationary (CS) regime, introducing CS-Colored-nLIM. The proposed method constructs a periodic, colored-noise-forced, quadratic stochastic system from cyclostationary input data. In this formulation, the active nonlinear components can be empirically determined through a sparse identification scheme specifically developed for colored-noise-forced systems. Application to climate prediction demonstrates that CS-Colored-nLIM achieves predictive performance comparable to modern machine learning and statistical models, while offering greater flexibility with moderate computational demand, making it potentially applicable to a broader range of complex systems beyond climate dynamics.

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Phys. Rev. Research 8, 023178– Published 18 May, 2026
  • Received 19 December 2025
  • Accepted 6 April 2026
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