@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0217},
url = {http://global-sci.org/intro/article_detail/cicp/20787.html}
}