# Enabling Real-Time Training of a Wildfire-to-Smoke Map with Multilinear Operators

arXiv: https://arxiv.org/abs/2605.04164 · HTML: https://mlsanity.com/paper/2605.04164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 97 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 19 of 19)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Next Day Wildfire Spread: A Machine Learning Data Set to Predict Wildfire Spreading from Remote-Sensing Data](https://mlsanity.com/paper/2112.02447/) (2021)
- [Neural and spectral operator surrogates: unified construction and expression rate bounds](https://mlsanity.com/paper/2207.04950/) (2022)
- [Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks](https://mlsanity.com/paper/2307.11013/) (2023)
- [Nonlinear integro-differential operator regression with neural networks](https://mlsanity.com/paper/1810.08552/) (2018)
- [Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning](https://mlsanity.com/paper/2407.00809/) (2024)
- [Improved Wildfire Spread Prediction with Time-Series Data and the WSTS+ Benchmark](https://mlsanity.com/paper/2502.12003/) (2025)
- [Polynomial Chaos Expansion for Operator Learning](https://mlsanity.com/paper/2508.20886/) (2025)
- [Performance of Neural and Polynomial Operator Surrogates](https://mlsanity.com/paper/2604.00689/) (2026)
- [Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts](https://mlsanity.com/paper/2309.02615/) (2023)
- [Verification and Validation for Trustworthy Scientific Machine Learning](https://mlsanity.com/paper/2502.15496/) (2025)
- [A spatial causal analysis of wildland fire-contributed PM2.5 using numerical model output](https://mlsanity.com/paper/2003.06037/) (2020)
- [Toward real-time optimization through model reduction and model discrepancy sensitivities](https://mlsanity.com/paper/2508.21792/) (2025)

## Abstract (arXiv)

Wildfires are a major producer of fine particulate matter, impacting human health and the electrical grid. Accurately forecasting smoke impacts over long time scales incorporates fuel treatment strategies, natural fuel succession, and stochastic events like lightning strikes. However, predicting smoke for each fuel distribution with a forward simulation of a coupled fire-atmosphere model is computationally infeasible. Moreover, relatively simple fire models are tractable to run in many long-time scenarios but do not capture smoke transport. We use data-driven multilinear operators to predict a smoke concentration field from knowledge of the time since ignition for two quantities of interest: aerosol optical depth and smoke detection. Our method first computes the principal components of time-since-ignition and smoke concentration fields and then learns a map from powers of the input coefficients to the output coefficients. We apply our learned operator to smoke prediction in the Upper Rio Grande Watershed. After collecting training data, learning the approximation weights on a CPU takes less than 30 seconds, and each forward call takes less than 1 ms. On a proxy for aerosol optical depth, we obtain equal accuracy to Monte Carlo sampling with fewer than half as many coupled model calls. For smoke detection, we obtain an intersection-over-union (IoU) of 0.64 and an area under the receiver operating characteristic curve (AUC) of 0.95 on holdout data. Our method is significantly more accurate than the most similar published smoke classifier, which obtains an IoU and AUC of 0.15 and 0.61, respectively, on a 2015 bushfire in Australia.