  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.
