Post Processing Sparse And Instantaneous 2D Velocity Fields Using Physics-Informed Neural Networks

This work tackles the problem of resolving high-resolution velocity fields from a set of sparse off-grid observations.  We follow the framework of Physics-Informed Neural Networks where simple Multi-layer Perceptor (MLP) are trained to solve partial differential equations (PDEs). In contrast with other state-of-the-art methods based of Convolutional Neural Networks, these models can be applied to super-resolve sparse Lagrangian velocity measurements. Moreover, such a framework can be easily extended to output divergence-free quantities and offer simple implementation of prior physical as regularization terms. In particular, we employ a sub-grid model based on structure-functions to improve the accuracy of the super-resolved velocity fields of turbulent flows. Numerical experimentation on synthetic data shows that the proposed approach can accurately reconstruct dense Eulerian velocity fields from sparse Lagrangian velocity measurements.