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 Network...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.展开更多
基金This work was supported by National Science Foundation under grant DMS-2012469.
文摘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.
