Nonlinear Reduced DNN Models for State Estimation

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