Nonlinear Reduced DNN Models for State Estimation (Communications in Computational Physics, 2022)
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.
Keywords: State estimation in model-compliant norms; deep neural networks; sensor coordinates; reduced bases; ResNet structures; network expansion.