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. 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.
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global parameters from variations in an identified model using only observational data. This capability, when paired with first principles analysis, can effectively distinguish the effects of these changing parameters from the intrinsic complexity of the system. Here we illustrate this by identifying a set of governing equations for an experiment generating a weakly turbulent fluid flow, then analyzing variation in the coefficients of these equations to unravel the drift in its physical parameters.
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