Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subsets in state system starting from an subset based on spectral properties Koopman operator. When evolution is known locally several system, stitching result derived that yields Additionally, case equivariant systems, developed identify using symmetry between and time-series data any one subsets. Finally, these results are extended topologically conjugate systems; particular, relation tuple systems established. The proposed demonstrated second-order nonlinear including bistable toggle switch. Our method elucidates strategy designing discovery experiments: experiment execution can be done many steps, models different combined approximate