Two methods to approximate the Koopman operator with a reservoir computer

The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, wealth numerical methods providing finite-dimensional approximations have been proposed [e.g., extended dynamic mode decomposition (EDMD) and its variants]. While convergence results EDMD require an infinite number dictionary elements, recent studies shown that only elements can yield efficient approximation operator, provided they are well-chosen through proper training process. However, this process typically relies on nonlinear optimization techniques. paper, we propose two novel based reservoir computer to train dictionary. These rely solely linear convex optimization. We illustrate efficiency method with several examples in context data reconstruction, prediction, computation spectrum. pave way use framework.