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

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 spatiallyextended 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.

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

“…For instance, an equation describing the evolution of momentum for a weakly turbulent flow in a thin layer of fluid could be identified from either synthetic [5] or exper-imental data [6] after the form of the equation was constrained by a few extremely general physical constraints: smoothness, locality, and the relevant symmetries. For nonrelativistic systems, the symmetries include translations in time and Euclidean symmetry (translations, rotations, and reflections) in space.…”

“…In order to obtain a parsimonious model, we must find a sparse coefficient vector c * such that the residual Qc * is comparable to the residual Qc with c given by (6). If the parsimonious model contains multiple terms, it can usually be identified by an iterative greedy algorithm.…”