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Learning Invariant Subspaces of Koopman Operators--Part 2: Heterogeneous Dictionary Mixing to Approximate Subspace Invariance
Charles A. Johnson, Shara Balakrishnan, Enoch Yeung
This work builds on the models and concepts presented in part 1 to learn approximate dictionary representations of Koopman operators from data. Part I of this paper presented a met…
Learning Invariant Subspaces of Koopman Operators--Part 1: A Methodology for Demonstrating a Dictionary's Approximate Subspace Invariance
Charles A. Johnson, Shara Balakrishnan, Enoch Yeung
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and i…
Data-Driven Observability Decomposition with Koopman Operators for Optimization of Output Functions of Nonlinear Systems
Shara Balakrishnan, Aqib Hasnain, Robert Egbert +1
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state d…
Heterogeneous mixtures of dictionary functions to approximate subspace invariance in Koopman operators
Charles A. Johnson, Shara Balakrishnan, Enoch Yeung
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and i…