arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.01680cs.NEcs.NAmath.NA
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基于进化方法的数据驱动物理方程发现

The data-driven physical-based equations discovery using evolutionary approach

Alexander Hvatov, Mikhail Maslyaev

摘要:

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,解释起来就越困难。本文描述了从给定的观测数据中发现数学方程的算法。该算法将遗传编程与稀疏回归相结合。该算法允许获得不同形式的结果模型。作为一个例子,它可以用于管理分析方程发现以及偏微分方程(PDE)发现。其主要思想是收集一袋积木(它可以是简单的函数或它们的任意阶导数),然后从袋子中取出它们来创建组合,这些组合将代表最终方程的项。选择的术语传递到进化算法,该算法用于进化选择。将进化步骤与稀疏回归相结合,以仅选择重要项。因此,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。文中给出了该算法的两个应用实例:海洋气象过程的偏微分方程发现和声学过程的函数发现。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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