Leveraging Koopman operator and Deep Neural Net-works for Parameter Estimation and Future Prediction of Duffing oscillators

The exploration of nonlinear dynamical systems holds significant importance across scientific and engineering disciplines, primarily for its applications in modeling real-world phenomena. Traditional methods employed for the analysis and prediction of the behavior of these systems typically involve intricate mathematical techniques and numerical simulations. This paper pre-sents an innovative approach that combine the capabilities of the Koopman operator and deep neural networks to establish a linear representation of the Duffing oscillator. This newly de-veloped methodology facilitates effective parameter estimation and the accurate prediction of the oscillator s future behavior. Moreover, the paper proposes a modified training procedure aimed at confining the Koopman operator to a linear layer within the neural network, as op-posed to its application across the entire network. This synergy between the Koopman operator and deep neural networks not only simplifies the analysis of nonlinear systems but also paves the way for significant advancements in predictive modeling across diverse fields.