The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. This algorithm allows obtaining different forms of the resulting models. As an example, it could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery. The main idea is to collect a bag of the building blocks (it may be simple functions or their derivatives of arbitrary order) and consequently take them from the bag to create combinations, which will represent terms of the final equation. The selected terms pass to the evolutionary algorithm, which is used to evolve the selection. The evolutionary steps are combined with the sparse regression to pick only the significant terms. As a result, we obtain a short and interpretable expression that describes the physical process that lies beyond the data. In the paper, two examples of the algorithm application are described: the PDE discovery for the metocean processes and the function discovery for the acoustics.

中文翻译：

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使用进化方法的数据驱动的基于物理的方程发现

现代机器学习方法允许人们以各种方式获得数据驱动的模型。然而，模型越复杂，就越难解释。在论文中，我们描述了从给定的观测数据中发现数学方程的算法。该算法将遗传规划与稀疏回归相结合。该算法允许获得不同形式的结果模型。例如，它可用于管理分析方程发现以及偏微分方程 (PDE) 发现。主要思想是收集一袋积木（它可能是简单的函数或其任意顺序的衍生物），然后从袋中取出它们以创建组合，这将代表最终方程的项。选定的术语传递给进化算法，用于进化选择。进化步骤与稀疏回归相结合以仅选择重要项。结果，我们获得了一个简短且可解释的表达式，它描述了数据之外的物理过程。在本文中，描述了算法应用的两个例子：气象海洋过程的 PDE 发现和声学的函数发现。