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Abstract:
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As data-centric engineering expands and we proceed to collect, store, and manipulate data in more prolific quantities, the ability to automatically extract governing equations from this information remains a crucial challenge. Currently, scientists construct generalized linear models manually to identify, expand, and forecast these systems over time, a process known as system identification. Here, the only assumption is that just a few essential terms regulate the underlying structure's dynamics, which holds for many physical systems (Brunton et al., 2016). In this work, we employ several variable selection methods to automatically extract a sparse solution for these dynamic equations to accurately visualize and interpret the data. We outline our Automatic Sparse Regression (TAPER) algorithm, which provides an iterative process that implements various statistical learning methods to extract governing equations from data. The TAPER algorithm develops a fully automated process for identifying the Lorenz chaotic system with a precision that offers advancement to state-of-the-art semi-automated methods by at least one order of magnitude (Brunton et al., 2016).
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