Regression-Based Projection for Learning Mori–Zwanzig Operators

Lin, Yen Ting; Tian, Yifeng; Perez, Danny; Livescu, Daniel

doi:10.1137/22m1506146

Regression-Based Projection for Learning Mori–Zwanzig Operators

Journal Article · Fri Oct 13 00:00:00 EDT 2023 · SIAM Journal on Applied Dynamical Systems

DOI:https://doi.org/10.1137/22m1506146· OSTI ID:2203394

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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 method 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 is a higher-order approximate Koopman learning method. We show that more expressive nonlinear regression models naturally fill in the gap between the highly idealized and computationally efficient Mori’s projection operator and the most optimal yet computationally infeasible Zwanzig’s projection operator. We performed numerical experiments and extracted the operators for an array of regression-based projections, including linear, polynomial, spline, and neural network–based regressions, showing a progressive improvement as the complexity of the regression model increased. In conclusion, our proposition provides a general framework to extract memory-dependent corrections and can be readily applied to an array of data-driven learning methods for stationary dynamical systems in the literature.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2203394

Alternate ID(s):: OSTI ID: 2202613
OSTI ID: 2202615

Report Number(s):: LA-UR--22-24323

Journal Information:: SIAM Journal on Applied Dynamical Systems, Journal Name: SIAM Journal on Applied Dynamical Systems Journal Issue: 4 Vol. 22; ISSN 1536-0040

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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