论文标题
DLGA-PDE：通过深度学习和遗传算法的组合发现具有不完整候选库的PDE
DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
论文作者
论文摘要
最近已经开发出数据驱动的方法来发现物理问题的基本部分微分方程（PDE）。但是，对于这些方法，通常需要在PDE中使用潜在术语的完整候选库。为了克服这一局限性，我们提出了一个新的框架，结合了深度学习和遗传算法（称为DLGA-PDE），用于发现PDE。在提出的框架中，使用了一个经过物理问题的可用数据训练的深神经网络来生成元数据并计算衍生物，然后使用遗传算法来发现基本的PDE。由于遗传算法的优点，例如突变和交叉，DLGA-PDE可以与不完整的候选库一起使用。对提出的DLGA-PDE进行了测试，以发现Korteweg-de Vries（KDV）方程，汉堡方程，波动方程和Chaffee-Infante方程，以进行概念证明。即使在存在嘈杂和有限的数据的情况下，也无需完整的候选库即可获得令人满意的结果。
Data-driven methods have recently been developed to discover underlying partial differential equations (PDEs) of physical problems. However, for these methods, a complete candidate library of potential terms in a PDE are usually required. To overcome this limitation, we propose a novel framework combining deep learning and genetic algorithm, called DLGA-PDE, for discovering PDEs. In the proposed framework, a deep neural network that is trained with available data of a physical problem is utilized to generate meta-data and calculate derivatives, and the genetic algorithm is then employed to discover the underlying PDE. Owing to the merits of the genetic algorithm, such as mutation and crossover, DLGA-PDE can work with an incomplete candidate library. The proposed DLGA-PDE is tested for discovery of the Korteweg-de Vries (KdV) equation, the Burgers equation, the wave equation, and the Chaffee-Infante equation, respectively, for proof-of-concept. Satisfactory results are obtained without the need for a complete candidate library, even in the presence of noisy and limited data.
