Machine learning in parameter estimation of nonlinear systems

TL;DR

This paper introduces a neural network approach using Huber loss for accurate parameter estimation in complex nonlinear systems, validated across various dynamical models with noisy data.

Contribution

It presents a novel neural network method leveraging Huber loss for robust parameter estimation in nonlinear systems, demonstrating effectiveness across multiple models.

Findings

Accurately estimates parameters in nonlinear systems.

Robust to noise and uncertainties.

Effective across diverse dynamical models.

Abstract

Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps into deep learning's abilities to uncover parameters governing intricate behaviors in nonlinear equations. We validate our approach using synthetic data and predefined functions that model system dynamics. By training the neural network with noisy time series data, it fine-tunes the Huber loss function to converge to accurate parameters. We apply our method to damped oscillators, Van der Pol oscillators, Lotka-Volterra systems, and Lorenz systems under multiplicative noise. The trained neural network accurately estimates parameters, evident from closely matching latent dynamics. Comparing true and estimated trajectories visually reinforces our method's precision and robustness. Our study underscores the Huber loss-guided neural network as a versatile tool for parameter estimation, effectively uncovering complex relationships in nonlinear systems. The method navigates noise and uncertainty adeptly, showcasing its adaptability to real-world challenges.