论文标题
使用进化方法的数据驱动的基于物理的方程发现
The data-driven physical-based equations discovery using evolutionary approach
论文作者
论文摘要
现代的机器学习方法允许人们以各种方式获得数据驱动的模型。但是，模型越复杂，它就越难解释。在本文中，我们从给定的观测数据数据中描述了数学方程发现的算法。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。例如，它可用于管理分析方程发现以及部分微分方程（PDE）发现。 主要思想是收集一袋构建块（可能是简单的功能或其任意顺序的衍生物），因此将它们从包中取出来创建组合，这将代表最终方程式的术语。选定的术语传递到用于进化选择的进化算法。进化步骤与稀疏回归相结合，仅选择重要术语。结果，我们获得了一个简短且可解释的表达，该表达式描述了超出数据的物理过程。 在本文中，描述了算法应用程序的两个示例：Metocean过程的PDE发现和声学的功能发现。
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.
