Machine learning in parameter estimation of nonlinear systems - Kumar, Kaushal; Kostina, Ekaterina (The European physical journal. B, Condensed matter and complex systems, 2025)
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.
Gesehen am 26.09.2025