论文标题
使用提取的物理特征对2D部分微分方程的数据驱动识别
Data-driven Identification of 2D Partial Differential Equations using extracted physical features
论文作者
论文摘要
许多科学现象是通过部分微分方程（PDE）建模的。数据收集工具的开发以及机器学习的进步（ML）技术增加了从实验观察到的数据中对数据驱动的识别等方程的机会。我们提出了一种ML方法，以从二维时空数据中发现方程中涉及的术语。从数据样本中提取了鲁棒和有用的物理特征，以表示方程中每个数学术语施加的特定行为。与以前的模型相比，这个想法使我们能够通过不同订单的时间导数发现2D方程，并确定未经培训模型的新的基础物理学。此外，该模型可以与少量低分辨率数据一起使用，同时避免数值差异。结果表明，与三维卷积神经网络（3D CNN）自动检测到的特征相比，根据先验知识提取的特征的鲁棒性。尽管在这项工作中研究了特定的PDE，但可以扩展提出方法的概念以可靠地识别各种PDE。
Many scientific phenomena are modeled by Partial Differential Equations (PDEs). The development of data gathering tools along with the advances in machine learning (ML) techniques have raised opportunities for data-driven identification of governing equations from experimentally observed data. We propose an ML method to discover the terms involved in the equation from two-dimensional spatiotemporal data. Robust and useful physical features are extracted from data samples to represent the specific behaviors imposed by each mathematical term in the equation. Compared to the previous models, this idea provides us with the ability to discover 2D equations with time derivatives of different orders, and also to identify new underlying physics on which the model has not been trained. Moreover, the model can work with small sets of low-resolution data while avoiding numerical differentiations. The results indicate robustness of the features extracted based on prior knowledge in comparison to automatically detected features by a Three-dimensional Convolutional Neural Network (3D CNN) given the same amounts of data. Although particular PDEs are studied in this work, the idea of the proposed approach could be extended for reliable identification of various PDEs.
