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Volume 32, Issue 1
Nonlinear Reduced DNN Models for State Estimation

Wolfgang Dahmen, Min Wang & Zhu Wang

DOI: 10.4208/cicp.OA-2021-0217

Commun. Comput. Phys., 32 (2022), pp. 1-40.

Published online: 2022-07

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  • Abstract

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

  • Keywords

State estimation in model-compliant norms, deep neural networks, sensor coordinates, reduced bases, ResNet structures, network expansion.

  • AMS Subject Headings

65N20, 65N21, 68T07, 35J15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-1, author = {Dahmen , WolfgangWang , Min and Wang , Zhu}, title = {Nonlinear Reduced DNN Models for State Estimation}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {1}, pages = {1--40}, abstract = {

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0217}, url = {http://global-sci.org/intro/article_detail/cicp/20787.html} }
TY - JOUR T1 - Nonlinear Reduced DNN Models for State Estimation AU - Dahmen , Wolfgang AU - Wang , Min AU - Wang , Zhu JO - Communications in Computational Physics VL - 1 SP - 1 EP - 40 PY - 2022 DA - 2022/07 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2021-0217 UR - https://global-sci.org/intro/article_detail/cicp/20787.html KW - State estimation in model-compliant norms, deep neural networks, sensor coordinates, reduced bases, ResNet structures, network expansion. AB -

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

Dahmen , WolfgangWang , Min and Wang , Zhu. (2022). Nonlinear Reduced DNN Models for State Estimation. Communications in Computational Physics. 32 (1). 1-40. doi:10.4208/cicp.OA-2021-0217
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