Automated transport separation using the neural shifted proper orthogonal decomposition
This addresses a limitation in shifted proper orthogonal decomposition methods for real-life problems where transport operators are unknown, offering an automated solution for fields like wildfire modeling.
The paper tackles the problem of decomposing transport-dominated fields without prior knowledge of transport operators by introducing a neural network-based method that simultaneously estimates transport and co-moving fields, demonstrating effective separation in synthetic data and a wildland fire model.
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.