Dual systems identification methods based on Koopman operator theory

We report our recent developments on Koopman operator lifting techniques for system identification and parameter estimation. We present two methods, which are based on the key idea of identifying the Koopman operator in a lifted space of observables, but rely on two different finite-dimensional approximations of the Koopman operator. The first method is a parametric technique which reconstructs the vector field using a dictionary of library functions. The second method can be seen as a dual approach and provides estimates of the vector field at the data points. We compare the performances of these two methods and consider large
dimensional systems. Theoretical convergence results are also provided.