Robust dominant balance analysis for identifying governing flow physics in experimental settings

Deploying unsupervised learning in the context of system identification, the data-driven dominant balance algorithm extracts a low-dimensional representation of the dominant physical processes underlying high-dimensional fluid flow data. While the original implementation proved to be successful in extracting sparse representations from time-averaged DNS data, it is not able to adequately identify governing patterns in more challenging conditions, e.g., instantaneous dynamics, noisy measurement data, and measurement uncertainties. We address these issues by taking an ensemble approach to stabilize the unsupervised learning process and provide a measure of uncertainty quantification. Moreover, we leverage the integral form of the governing equations to cast a "weak form" of the problem which lends additional noise robustness to our algorithm and circumvents the challenging determination of gradients in experimental settings. The effectiveness of this novel formulation is demonstrated on a variety of numerical and experimental test cases including transitional boundary layer flows, wall-bounded turbulence with favorable and adverse pressure gradients, and shock-dominated configurations such as the viscous Burgers' equation.