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.

翻译：在本文中,我们提出了一个数据驱动国家估算计划,为PDEs的参数家庭生成非线性减少模型,直接提供以深神经网络为代表的数据到国家地图,一个主要成份是传感器引发的符合模型的希尔伯特空间分解,该空间在问题相关指标中需要近似,与基于“缩小基础”概念的国家测算员参数背景数据弱化框架的作用相似。 广泛的数字测试揭示了提高这类测算员的稳健性和性能的若干优化战略。