This paper presents a neural network-based methodology for the decomposition of transport-dominated fields using the shifted proper orthogonal decomposition (sPOD). Classical sPOD methods typically require an a priori knowledge of the transport operators to determine the co-moving fields. However, in many real-life problems, such knowledge is difficult or even impossible to obtain, limiting the applicability and benefits of the sPOD. To address this issue, our approach estimates both the transport and co-moving fields simultaneously using neural networks. This is achieved by training two sub-networks dedicated to learning the transports and the co-moving fields, respectively. Applications to synthetic data and a wildland fire model illustrate the capabilities and efficiency of this neural sPOD approach, demonstrating its ability to separate the different fields effectively.

翻译：本文提出了一种基于神经网络的方法，利用移位本征正交分解（sPOD）对以输运为主导的物理场进行分解。传统的sPOD方法通常需要先验已知输运算子以确定共动场，然而在许多实际问题中，此类知识难以甚至无法获取，从而限制了sPOD的适用性与优势。为解决此问题，我们的方法通过神经网络同时估计输运过程与共动场。该目标通过训练两个分别专注于学习输运过程与共动场的子网络实现。在合成数据与野火模型中的应用验证了该神经sPOD方法的性能与效率，证明了其有效分离不同物理场的能力。