论文标题
发现具有递归深神经网络的管理方程式
Discovery of Governing Equations with Recursive Deep Neural Networks
论文作者
论文摘要
数十年来，基于现有数据的模型发现一直是数学建模者的主要重点之一。尽管从适当数据中实现了模型识别的巨大成就，但如何从有限数据中解散模型的解决方案却很少解决。在本文中，当数据没有在时间上有效采样时，我们将重点关注模型发现问题。由于实验性可及性和人工/资源限制，这很常见。具体而言，我们引入了一个递归深度神经网络（RDNN），以进行数据驱动的模型发现。这种递归方法可以简单有效地检索管理方程式，并且可以通过增加递归阶段来显着提高近似准确性。特别是，当现有数据以较大的时间滞后采样时，我们提出的方法显示出了卓越的力量，传统方法可能无法从中恢复模型。动态系统的几个广泛使用的示例用于基准这种新提出的递归方法。数值比较证实了该递归神经网络在模型发现中的有效性。
Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less resolved. In this paper, we focus on the model discovery problem when the data is not efficiently sampled in time. This is common due to limited experimental accessibility and labor/resource constraints. Specifically, we introduce a recursive deep neural network (RDNN) for data-driven model discovery. This recursive approach can retrieve the governing equation in a simple and efficient manner, and it can significantly improve the approximation accuracy by increasing the recursive stages. In particular, our proposed approach shows superior power when the existing data are sampled with a large time lag, from which the traditional approach might not be able to recover the model well. Several widely used examples of dynamical systems are used to benchmark this newly proposed recursive approach. Numerical comparisons confirm the effectiveness of this recursive neural network for model discovery.
