Discovering dimensionless relations from data in complex fluids
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Machine learning has shown great promise in discovering differential equations from data over the past decade, offering an interpretable approach to extracting meaningful physics from observations, particularly in complex systems where deriving equations manually is infeasible. However, the application of such methods to real-world systems remains limited. In this work, we demonstrate the discovery of a normal form equation governing non-Newtonian fluids, along with the identification of relevant dimensionless groups that control the bifurcation behavior of the system. Our approach combines sparse identification of nonlinear dynamics (SINDy) with neural networks, while incorporating the Buckingham Pi theorem as a constraint to ensure the discovery of dimensionless groups. We propose innovative techniques that expand the applicability of machine learning in extracting interpretable physics from complex materials where data is available and theory is lacking.
