Machine learning in parameter estimation of nonlinear systems

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.

Forecasting Crude Oil Prices Using Reservoir Computing Models

Accurate crude oil price prediction is crucial for financial decision-making. We propose a novel reservoir computing model for forecasting crude oil prices. It outperforms popular deep learning methods in most scenarios, as demonstrated through rigorous evaluation using daily closing price data from major stock market indices. Our model's competitive advantage is further validated by comparing it with recent deep-learning approaches. This study introduces innovative reservoir computing models for predicting crude oil prices, with practical implications for financial practitioners. By leveraging advanced techniques, market participants can enhance decision-making and gain valuable insights into crude oil market dynamics.