Automated transport separation using the neural shifted proper orthogonal decomposition

TL;DR

This paper introduces a neural network-based method for decomposing transport-dominated fields without prior knowledge of transport operators, enhancing the applicability of shifted proper orthogonal decomposition in complex real-world problems.

Contribution

The paper proposes a novel neural sPOD approach that estimates transport and co-moving fields simultaneously, removing the need for pre-known transport operators.

Findings

Effective separation of fields demonstrated on synthetic data

Successful application to a wildland fire model

Neural sPOD improves decomposition efficiency and accuracy

Abstract

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.