Parametric model order reduction for a wildland fire model via the shifted POD based deep learning method

TL;DR

This paper introduces a non-intrusive, data-driven model order reduction method combining shifted POD and deep learning to efficiently and accurately simulate wildland fire models with varying parameters.

Contribution

It presents a novel integration of shifted POD with deep learning for parametric model reduction of transport-dominated phenomena, improving accuracy and speed.

Findings

Achieves percent-range accuracy in wildland fire simulations.

Enables rapid predictions within seconds.

Demonstrates effectiveness on 1D and 2D fire models.

Abstract

Parametric model order reduction techniques often struggle to accurately represent transport-dominated phenomena due to a slowly decaying Kolmogorov n-width. To address this challenge, we propose a non-intrusive, data-driven methodology that combines the shifted proper orthogonal decomposition (POD) with deep learning. Specifically, the shifted POD technique is utilized to derive a high-fidelity, low-dimensional model of the flow, which is subsequently utilized as input to a deep learning framework to forecast the flow dynamics under various temporal and parameter conditions. The efficacy of the proposed approach is demonstrated through the analysis of one- and two-dimensional wildland fire models with varying reaction rates, and its performance is evaluated using multiple error measures. The results indicate that the proposed approach yields highly accurate results within the percent range, while also enabling rapid prediction of system states within seconds.