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Machine learning in parameter estimation of nonlinear systems

Accurate parameter estimation in nonlinear dynamical systems remains a fundamental challenge due to noise, limited data, and model complexity. Traditional methods, such as gradient-based optimization and nonlinear least squares (NLS), often struggle under real-world multiplicative noise, exhibiting...

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Hauptverfasser: Kumar, Kaushal (VerfasserIn) , Kostina, Ekaterina (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 09 April 2025
In: The European physical journal. B, Condensed matter and complex systems
Year: 2025, Jahrgang: 98, Heft: 4, Pages: 1-18
ISSN:1434-6036
DOI:10.1140/epjb/s10051-025-00904-7
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1140/epjb/s10051-025-00904-7
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Verfasserangaben:Kaushal Kumar and Ekaterina Kostina

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520 |a Accurate parameter estimation in nonlinear dynamical systems remains a fundamental challenge due to noise, limited data, and model complexity. Traditional methods, such as gradient-based optimization and nonlinear least squares (NLS), often struggle under real-world multiplicative noise, exhibiting sensitivity to outliers and high computational demands. This study introduces a neural network framework integrating the Huber loss function to achieve robust and efficient parameter estimation. Applied to canonical dynamical systems, including damped oscillators, van der Pol oscillators, Lotka-Volterra models, and chaotic Lorenz dynamics, the proposed method demonstrates superior accuracy and resilience to noise. Notably, it maintains sub-1.2\% relative errors for key parameters in the Lorenz system, significantly outperforming NLS, which diverges with errors exceeding 12% under identical noise conditions. The use of SiLU activation improves convergence, yielding statistically significant reductions in estimation errors (p < 0.01). Furthermore, the framework operates up to 8 X faster than conventional optimization techniques while reducing root-mean-square error by over 99.9% in high-noise regimes. These results establish a robust, data-driven approach for parameter estimation in complex dynamical systems, bridging machine learning with nonlinear physics and enabling real-time applications in noisy environments. 
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