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Chapitre D'ouvrage Année : 2022

State Estimation—The Role of Reduced Models

Wolfgang Dahmen
  • Fonction : Auteur
Ron Devore
  • Fonction : Auteur

Résumé

Abstract The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations and (ii) data provided by measurement devices or sensors . The amount of sensors is typically limited and data acquisition may be expensive and in some cases even harmful. This article reviews some recent developments for this “small-data” scenario where inversion is strongly aggravated by the typically large parametric dimensionality. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic accuracy quantification related to the required computational complexity. We discuss optimality criteria which delineate intrinsic information limits, and highlight the role of reduced models for developing efficient computational strategies. In particular, the need to adapt the reduced models—not to a specific (possibly noisy) data set but rather to the sensor system—is a central theme. This, in turn, is facilitated by exploiting geometric perspectives based on proper stable variational formulations of the continuous model.

Dates et versions

hal-03884757 , version 1 (05-12-2022)

Identifiants

Citer

Albert Cohen, Wolfgang Dahmen, Ron Devore. State Estimation—The Role of Reduced Models. Recent Advances in Industrial and Applied Mathematics, 1, Springer International Publishing, pp.57-77, 2022, SEMA SIMAI Springer Series, ⟨10.1007/978-3-030-86236-7_4⟩. ⟨hal-03884757⟩
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