Manifold learning techniques and model reduction applied to dissipative PDEs
Computational Physics
2010-11-24 v1 Dynamical Systems
Abstract
We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a `"nonlinear extension" of the POD-Galerkin approach to obtaining reduced dynamic models of dissipative evolution equations. The approach is illustrated through a reaction-diffusion PDE, and the performance of different simulators on the full and the reduced models is compared. We also discuss the relation of this nonlinear extension with the so-called "nonlinear Galerkin" methods developed in the context of Approximate Inertial Manifolds.
Cite
@article{arxiv.1011.5197,
title = {Manifold learning techniques and model reduction applied to dissipative PDEs},
author = {Benjamin E. Sonday and Amit Singer and C. William Gear and Ioannis G. Kevrekidis},
journal= {arXiv preprint arXiv:1011.5197},
year = {2010}
}
Comments
20 pages, 8 figures