Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

TL;DR

This paper introduces SPIDER, a hybrid data-driven method that learns governing fluid dynamics equations from turbulent flow data using physical assumptions, weak formulations, and sparse regression, even with high noise levels.

Contribution

The paper presents a novel approach combining physical principles, weak formulations, and sparse regression to discover fluid physics equations from turbulent data, robust to noise.

Findings

Successfully extracted Navier-Stokes and related equations from turbulent data

Method remains accurate under high noise conditions

Provides interpretable PDEs that reveal physical effects and data quality

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 Navier-Stokes 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 well-suited to experimental data.