Nonlinear Reduced DNN Models for State Estimation

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