Manifold learning techniques and model reduction applied to dissipative PDEs

Details Manifold learning techniques and model reduction applied to dissipative PDEs Manifold learning techniques and model reduction applied to dissipative PDEs

2010-11-23

arxiv.org/abs/1011.5197v1

Physics

Computational Physics

20 pages, 8 figures

Scientific paper

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.

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