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Huyên Pham: Learning mappings on Wasserstein space with applications to mean-field problems

Time: Tue 2023-02-21 10.15 - 11.15

Location: 3721 (Lindstedtsvägen 25)

Participating: Huyên Pham (Paris)

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We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems.  Two classes of neural networks based on bin density and on cylindrical approximation, are proposed to learn these so-called mean-field functions,   and are theoretically supported by universal approximation theorems. We perform several numerical experiments for training these two mean-field neural networks, and show their accuracy and efficiency in the generalization error with various test distributions. Finally, we present different algorithms relying on mean-field neural networks for solving McKean-Vlasov control problems.    Based on joint work with Xavier Warin (EDF, Fime)