Koopman representations with irregular time intervals

• We propose a framework to recover Koopman eigenfunctions and eigenvalues for irregularly sampled data. • We show that a Koopman eigenfunction and eigenvalue can be recovered via a natural optimization problem. • We provide technical remarks on the anticipated challenge in optimization and suggest a procedure to address them. • Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. • Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction-recovery accuracy. Koopman operator theory has been widely applied to data assimilation problems of real systems governed by dynamics, as the theory allows for data-driven construction of modes of dynamical systems. In many modern problems, these modes often must be learned from data with irregular sampling intervals, as opposed to commonly used regularly sampled data. Here, we propose a framework to recover a Koopman eigenfunction–eigenvalue pair for irregularly sampled data. We show that a Koopman eigenpair can be recovered via a natural optimization problem. We provide technical remarks on the anticipated challenges in optimization and suggest a procedure to address them. Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction–recovery accuracy.