# Automated transport separation using the neural shifted proper orthogonal decomposition

arXiv: https://arxiv.org/abs/2407.17539 · HTML: https://mlsanity.com/paper/2407.17539/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 23 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 2 of 2)

- [The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations](https://mlsanity.com/paper/2108.06558/) (2021)
- [Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction](https://mlsanity.com/paper/2106.11381/) (2021)

## Abstract (arXiv)

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.