Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

TL;DR

This paper presents a hybrid approach combining data-driven methods with physical principles to accurately model complex, noisy, and incomplete high-dimensional experimental data, specifically applied to fluid dynamics.

Contribution

It introduces a physically constrained symbolic regression technique capable of discovering accurate models from challenging experimental data.

Findings

Successfully modeled turbulent fluid flow from velocity data

Reconstructed pressure and forcing fields from limited measurements

Demonstrated robustness to noise and data incompleteness

Abstract

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially-extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables -- the pressure and forcing field driving the flow.