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Big data and large-scale machine learning have had a profound impact onscience and engineering, particularly in fields focused on forecasting andprediction. Yet, it is still not clear how we can use the superior patternmatching abilities of machine learning models for scientific discovery. This isbecause the goals of machine learning and science are generally not aligned. Inaddition to being accurate, scientific theories must also be causallyconsistent with the underlying physical process and allow for human analysis,reasoning, and manipulation to advance the field. In this paper, we present acase study on discovering a new symbolic model for oceanic rogue waves fromdata using causal analysis, deep learning, parsimony-guided model selection,and symbolic regression. We train an artificial neural network on causalfeatures from an extensive dataset of observations from wave buoys, whileselecting for predictive performance and causal invariance. We apply symbolicregression to distill this black-box model into a mathematical equation thatretains the neural network's predictive capabilities, while allowing forinterpretation in the context of existing wave theory. The resulting modelreproduces known behavior, generates well-calibrated probabilities, andachieves better predictive scores on unseen data than current theory. Thisshowcases how machine learning can facilitate inductive scientific discovery,and paves the way for more accurate rogue wave forecasting.

Machine-Guided Discovery of a Real-World Rogue Wave Model