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Journal Articles International Journal for Numerical Methods in Engineering Year : 2018

Model Reduction from Partial Observations

Abstract

This paper deals with model order reduction of parametric partial differential equations (PPDE). We consider the specific setup where the solutions of the PPDE are only observed through a partial observation operator and address the task of finding a good approximation subspace of the solution manifold. We provide and study several tools to tackle this problem. We first identify the best worst-case performance achievable in this setup and propose simple procedures to approximate this optimal solution. We then provide, in a simplified setup, a theoretical analysis relating the achievable reduction performance to the choice of the observation operator and the prior knowledge available on the solution manifold.
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Dates and versions

hal-01394059 , version 1 (02-02-2024)

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Cédric Herzet, Patrick Héas, Angélique Drémeau. Model Reduction from Partial Observations. International Journal for Numerical Methods in Engineering, 2018, 113 (3), pp.479-511. ⟨10.1002/nme.5623⟩. ⟨hal-01394059⟩
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