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Mean-field neural networks: learning mappings on Wasserstein space. (arXiv:2210.15179v1 [math.OC])
Oct. 28, 2022, 1:13 a.m. | Huyên Pham, Xavier Warin
stat.ML updates on arXiv.org arxiv.org
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 …
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