IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Reduced basis methods and their application in data science and microbiome analysis

  • Oct. 19, 2015
  • 1:15 p.m.

Abstract

Models of reduced computational complexity is indispensable in scenarios where a large number of numerical solutions to a parametrized problem are desired in a fast/real-time fashion. These include simulation-based design, parameter optimization, optimal control, multi-model/scale analysis, uncertainty quantification. Thanks to an offline-online procedure and the recognition that the parameter-induced solution manifolds can be well approximated by finite-dimensional spaces, reduced basis method (RBM) and reduced collocation method (RCM) can improve efficiency by several orders of magnitudes. The accuracy of the RBM solution is maintained through a rigorous a posteriori error estimator whose efficient development is critical.

In this talk, I will give a brief introduction of the RBM, discuss recent and ongoing efforts to develop RCM, explain how the newly-designed Reduced Basis Decomposition can be used for data compression and face recognition, and also mention ongoing effort of applying RBM to microbiome analysis.

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