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  • Letter
  • Open Access

Nonlinear extensions of linear inverse models under memoryless or persistent random forcing

Justin Lien*

Hiroyasu Ando

  • Mathematical Institute, Tohoku University, 2 Chome-1-1 Katahira, Aoba Ward, Sendai, Miyagi 980-8577, Japan

  • Advanced Institute for Materials Research, Tohoku University, 2 Chome-1-1 Katahira, Aoba Ward, Sendai, Miyagi 980-8577, Japan and Mathematical Institute, Tohoku University, 2 Chome-1-1 Katahira, Aoba Ward, Sendai, Miyagi 980-8577, Japan

  • *Contact author: lien.justin.t8@dc.tohoku.ac.jp
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Phys. Rev. Research 7, L032038 – Published 20 August, 2025

DOI: https://doi.org/10.1103/ds1j-fx3v

Abstract

This study extends the linear inverse modeling (LIM) framework to nonlinear settings by presenting White-nLIM and Colored-nLIM, statistics-based empirical methods that construct approximate stochastic systems incorporating quadratic deterministic dynamics with either memoryless Gaussian white noise or persistent Ornstein-Uhlenbeck colored noise. Beyond the evident improvements over linear models, Colored-nLIM offers a robust approach to parameter estimation and statistical modeling under persistent stochastic forcing. Together with White-nLIM, these methods provide a systematic framework to assess the role of noise persistence in inverse modeling. Applications to the Lorenz 63 system and a simplified El Niño-Southern Oscillation model demonstrate their potential to capture chaotic behavior and climate variability.

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Phys. Rev. Research 7, L032038– Published 20 August, 2025
  • Received 8 April 2025
  • Accepted 28 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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