Web: http://arxiv.org/abs/2205.05135

May 12, 2022, 1:10 a.m. | Yen Ting Lin, Yifeng Tian, Daniel Livescu

stat.ML updates on arXiv.org arxiv.org

We propose to adopt statistical regression as the projection operator to
enable data-driven learning of the operators in the Mori--Zwanzig formalism. We
present a principled algorithm to extract the Markov and memory operators for
any regression models. We show that the choice of linear regression results in
a recently proposed data-driven learning algorithm based on Mori's projection
operator, which can be considered as a higher-order approximate Koopman
learning method. We show that more expressive, potentially nonlinear regression
models naturally fill …

arxiv learning math operators projection regression

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