Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks
This work addresses super-resolution for turbulent flows, a domain-specific problem in fluid dynamics, with incremental improvements through stabilization mechanisms.
The authors tackled the problem of zero-shot super-resolution for turbulent flows by proposing a neural network with embedded Luenberger-type observers and implicit forcing estimation, demonstrating its ability to recover unknown forcing and predict high-resolution flows from low-resolution noisy observations.
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.