Regression-based projection for learning Mori--Zwanzig operators. (arXiv:2205.05135v1 [math.DS])

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

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