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

通过因果分析、深度学习、遵循简约原则的模型选择和符号回归，本文通过一个案例研究展示了利用数据发现海洋罕见巨浪的新符号模型。该模型基于大量浮标观测数据上训练的人工神经网络，同时兼顾预测性能和因果不变性。我们将这个黑盒模型应用于符号回归，转化为数学方程，在现有波浪理论框架下进行解释，从而实现模型的预测能力和可解释性。结果表明，该模型能够重现已知行为，生成良好校准的概率，并在未见数据上取得更好的预测准确性，为罕见巨浪预测提供更准确的方法。