Machine learning in parameter estimation of nonlinear systems
This addresses the problem of accurate parameter estimation in complex nonlinear systems for scientific and engineering fields, but it is incremental as it builds on existing neural network methods with a specific loss function.
The paper tackled parameter estimation in nonlinear systems by using a neural network with the Huber loss function, achieving accurate parameter estimates as shown by closely matching latent dynamics in systems like damped oscillators and Lorenz systems under multiplicative noise.
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.