We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to provide error correction and stabilization mechanisms. In addition, to compensate for decrease of observer's performance due to the presence of unknown destabilizing forcing, the network is designed to estimate the contribution of the unknown forcing implicitly from the data over the course of training. By running a set of numerical experiments, we demonstrate that the proposed network does recover unknown forcing from data and is capable of predicting turbulent flows in high resolution from low resolution noisy observations.

翻译：我们提出一个新的神经网络设计,以解决动荡流动的零发超解问题。我们将Luenberger型观察者嵌入网络的架构,以告知该过程的物理网络,并提供错误纠正和稳定机制。此外,为了补偿观察员由于存在未知的破坏稳定的强迫而导致的性能下降,该网络旨在估算在培训过程中从数据中隐含的未知强迫作用。通过进行一系列数字实验,我们证明拟议的网络确实从数据中恢复了未知的强迫作用,并且能够预测低分辨率的噪音观测产生的高分辨率动荡流动。