Computational Mathematics and Scientific Computing Seminar

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Dimensionality Reduction of Nonlinear Waves Using Transport and Radon Transform

Speaker: Donsub Rim, Columbia University

Location: Warren Weaver Hall 1302

Date: Feb. 15, 2019, 10 a.m.

Synopsis:

Model reduction techniques allow the user to perform statistical studies of parametrized partial differential equations (PDEs). However, for hyperbolic PDEs the standard projection-based tools for model reduction fail due to the inherent lack of low-dimensional linear representation for the solution. In this talk, I will show that using monotone rearrangement from optimal transport can achieve dimensionality reduction for scalar nonlinear conservation laws. A multidimensional extension that combines this idea in 1D with the intertwining property of the Radon transform will be also discussed. This results in a generalization of the classical translational representation of Lax-Philips.