# Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction

arXiv: https://arxiv.org/abs/2106.11381 · HTML: https://mlsanity.com/paper/2106.11381/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [Nonlinear model reduction for transport-dominated problems](https://mlsanity.com/paper/2602.01397/) (2026)
- [Automated transport separation using the neural shifted proper orthogonal decomposition](https://mlsanity.com/paper/2407.17539/) (2024)

## Abstract (arXiv)

We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for advection-dominated systems. Furthermore, we discuss applying this new method to a wildland fire model whose dynamics feature traveling combustion waves and local ignition and is thus challenging for classical model reduction schemes based on linear subspaces. The new hyper-reduction framework allows us to construct parameter-dependent reduced-order models (ROMs) with efficient offline/online decomposition. The numerical experiments demonstrate that the ROMs obtained by the novel method outperform those obtained by a classical approach using the proper orthogonal decomposition and the discrete empirical interpolation method in terms of run time and accuracy.