Dynamic Representation of Optimal Transport via Ensemble Systems

Yi-Hsuan Shih, Wei Zhang, Jr-Shin Li

Primary Area: general machine learning (i.e., none of the above)

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Keywords: Optimal transport; ensemble systems; moment kernel representation

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Abstract: Optimal transport has gained widespread recognition in diverse areas from economics and fluid mechanics, lately, to machine learning. However, its connection and potential applications to the domain of dynamical systems and control remain underexplored. To fill this gap, we establish an ensemble-systems interpretation for modeling the optimal transport process. We interpret displacement interpolation of the transport between continuous distributions as a dynamic process and show that this can be modeled as an ensemble control system. This is achieved by establishing moment kernel representations for describing the dynamics of optimal transport and ensemble systems. This methodology further gives rise to an optimal transport based algorithm for learning controls for ensemble systems.

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Submission Number: 8757