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This work builds on the models and concepts presented in part 1 to learnapproximate dictionary representations of Koopman operators from data. Part Iof this paper presented a methodology for arguing the subspace invariance of aKoopman dictionary. This methodology was demonstrated on the state-inclusivelogistic lifting (SILL) basis. This is an affine basis augmented withconjunctive logistic functions. The SILL dictionary's nonlinear functions arehomogeneous, a norm in data-driven dictionary learning of Koopman operators. Inthis paper, we discover that structured mixing of heterogeneous dictionaryfunctions drawn from different classes of nonlinear functions achieve the sameaccuracy and dimensional scaling as the deep-learning-based deepDMD algorithm.We specifically show this by building a heterogeneous dictionary comprised ofSILL functions and conjunctive radial basis functions (RBFs). This mixeddictionary achieves the same accuracy and dimensional scaling as deepDMD withan order of magnitude reduction in parameters, while maintaining geometricinterpretability. These results strengthen the viability of dictionary-basedKoopman models to solving high-dimensional nonlinear learning problems.

Learning Invariant Subspaces of Koopman Operators--Part 2: Heterogeneous Dictionary Mixing to Approximate Subspace Invariance