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

Machine learning offers an intriguing alternative to first-principle 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.

Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits.

In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating that turbulent flows in both experiment and numerics transiently display time-periodic dynamics when they shadow unstable periodic orbits (UPOs). We show that UPOs we computed are also statistically significant, with turbulent flows spending a sizable fraction of the total time near these solutions.