Post Processing Sparse And Instantaneous 2D Velocity Fields Using Physics-Informed Neural Networks
D. Di Carlo (1), D. Heitz (2), T. Corpetti (1)
(1) Univ. de Rennes 2, LETG, CNRS, Rennes, France
(2) INRAE, OPAALE, Rennes, France
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.