Learning fluid physics from highly turbulent data using sparse physicsinformed discovery of empirical relations (SPIDER)
Abstract
We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality, and symmetry, a weak formulation of differential equations, and sparse regression. To illustrate this, we extract a system of governing equations describing flows of incompressible Newtonian fluids  the NavierStokes equation, the continuity equation, and the boundary conditions  from numerical data describing a highly turbulent channel flow in three dimensions. These relations have the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects as well as insight into the quality of the data, serving as a useful diagnostic tool. The approach described here is remarkably robust, yielding accurate results for very high noise levels, and should thus be wellsuited to experimental data.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2105.00048
 Bibcode:
 2021arXiv210500048G
 Keywords:

 Physics  Fluid Dynamics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Data Analysis;
 Statistics and Probability