Manifold learning techniques and model reduction applied to dissipative PDEs

Amit Singer; Benjamin E. Sonday; C. William Gear; Ioannis G. Kevrekidis

Manifold learning techniques and model reduction applied to dissipative PDEs

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arxiv 1011.5197 v1 pith:VBUHMOAI submitted 2010-11-23 physics.comp-ph math.DS

Manifold learning techniques and model reduction applied to dissipative PDEs

Benjamin E. Sonday , Amit Singer , C. William Gear , Ioannis G. Kevrekidis This is my paper

classification physics.comp-ph math.DS

keywords nonlineartechniquesapproachdissipativeequationsevolutionextensionlearning

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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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