Data-Driven Modeling of the Koopman-Oriented Chua Circuit Based on Reservoir Computers

Data-driven approaches based on nonlinear dynamical systems offer a strong framework for analyzing time series data. Among these methods, the Koopman operator is a powerful tool for data-driven analysis and decomposition of dynamical systems. In recent years, various numerical methods emerged to offer finite-dimensional approximations of this operator including the Hankel Alternative View of Koopman (HAVOK). Meanwhile, reservoir computing (RC) is a computational framework designed for processing temporal or sequential data. One of RC’s key advantages is its ability to effectively harness the dynamics of nonlinear systems for computational tasks. This paper introduces modifications to the RC-HAVOK algorithm, a recently proposed data-driven method that combines reservoir computing with HAVOK to approximate the Koopman operator. This approach efficiently reduces the size of the linear Koopman operator and achieves a lower error rate for modelling the Chua Circuit with a piece-wise linear (PWL) function. Results show that the modified RC-HAVOK outperforms the original RC-HAVOK methods in both accuracy and efficiency.