Machine learning in parameter estimation of nonlinear systems
Kaushal Kumar
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.