Physics-Informed Data-Driven Discovery of Quantities of Interest and Their Governing Equations
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We tackle two common challenges in discovering interpretable physics from data: 1) the identification of physics-informed quantities of interest and 2) the discovery of interpretable dynamics from incomplete measurements. We propose two approaches that constrain deep learning optimizers to identify physically-meaningful variables. This aims to merge the highly effective yet complex-to-understand feature learning of deep networks with the straightforward interpretability of physical laws. I will first highlight the importance of using dimensional-consistent learning and will propose techniques for data-driven discovery of dimensionless groups. In addition, I will demonstrate the use of deep delay double-encoders to recover full-state variables and their governing differential equations from partial measurements, with applications to fluid mechanics.
