Probabilistic Forecasting of Wildfire Size Using Conditional Flow Matching

arXiv:2610.15983 · cs.LG · Submitted 2026-10-11 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: Today's paper: "Probabilistic Forecasting of Wildfire Size Using Conditional Flow Matching".

Jane: The gist The proposed model presents a probabilistic model for predicting the temporal evolution of wildfire size using conditional generative algorithms, namely flow matching,

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So, to conclude on "Probabilistic Forecasting of Wildfire Size Using Conditional Flow Matching," this paper presents a probabilistic model for predicting the temporal evolution of wildfire size using conditional generative algorithms, specifically flow matching <ref:2610.15983#pg1>.

Jane: It claims that rather than predicting spatially resolved fire progression, this model forecasts a time series of fire acreage instead, which substantially reduces computational cost and enables efficient integration with downstream applications like early warning systems and risk assessment tools <ref:2610.15983#pg2>.

Lu: The authors argue that because the model is trained on data from WRF-SFIRE, it is able to represent the complex physical relationships present in that code <ref:2610.15983#pg3>. It’s bridging the gap between simulation fidelity and computational speed for acreage forecasting.

Meng: The practical takeaway for deployment is that this model offers a way to generate large ensembles of forecasts very quickly with minimal cost, which is exactly what we need for operational use <ref:2610.15983#pg3>. It’s about making complex wildfire prediction tools accessible for operational use.

Tom: And the performance validation shows that the model achieves a symmetric mean absolute percentage error sMAPE of zero point three nine for single-step predictions relative to reference WRF-SFIRE solutions <ref:2610.15983#pg2>.

Jane: And in recursive multi-step predictions over twenty-four hours, it achieved a final fire area sMAPE of zero point three nine while further providing meaningful quantification of forecast uncertainty <ref:2610.15983#pg2>.

Lu: So, the authors suggest integrating this into early warning systems or wildfire risk assessment tools where quantifying prediction uncertainty is critical <ref:2610.15983#pg3>. They also mentioned integration with plume rise models <ref:2610.15983#pg3>.

Meng: The final word is that the scalar formulation offers practical advantages over spatially resolved wildfire spread models, particularly in terms of computational cost and compatibility with downstream applications like plume rise models <ref:2610.15983#pg3>. It’s suitable for risk assessment and early warning tasks where quantification of prediction uncertainty is critical <ref:2610.15983#pg3>.

Conclusion: Tom: So, we've been looking at this paper, "Probabilistic Forecasting of Wildfire Size Using Conditional Flow Matching." Basically, they're using a new AI technique called flow matching to predict how big a wildfire will get over time.

Jane: It sounds complicated because it uses these generative algorithms, but the main thing is that instead of mapping out every single inch of fire on the map, it just gives you a timeline of acreage changes.

Lu: Right, and they're using conditional flow matching, which means they're training an AI to learn how to generate those future fire scenarios based on current conditions.

Meng: From what I see, the authors are feeding this model data from these WRF-SFIRE simulations and weather models from NAM. That’s their training set for this thing.

Lalam: The core idea they're pushing here is that you can get a time series of fire size predictions without having to run those massive, slow physics-based wildfire models every single time you want a forecast.

Tom: So what does it actually mean for someone who just needs an early warning system? Does it make things faster or more accurate?

Jane: It's about efficiency, Tom. They show that the model can predict the change in fire area over a three-hour interval, and they get a symmetric mean absolute percentage error of zero point thirty-nine for single steps.

Lu: And they also tackled longer timelines, doing recursive multi-step predictions over twenty-four hours for twelve test cases. The final fire area sMAPE was still zero point thirty-nine there.

Meng: That's the part I care about—the uncertainty quantification. They didn't just give you a single number; they gave you an ensemble of predictions, and they showed how that uncertainty grows over time.

Lalam: The paper suggests that this scalar approach is better than trying to predict every pixel of fire because it’s computationally much cheaper, which means it could be used for risk assessment tools on the ground.

Tom: So, in simple terms, this model lets us rapidly forecast wildfire size using machine learning instead of just running slow simulations.

Jane: Exactly. It turns a complex physical problem into a fast, probabilistic time series that you can plug directly into an early warning app or a risk tool.

Lu: The implication is that we might be able to get much faster, high-resolution forecasts for real-time decision making without needing supercomputer power for every scenario.

Meng: But the limitation they mention is that it’s currently working with spatially averaged weather conditions and terrain features, not the fine detail of every single fuel type or microclimate variation.

Lalam: So while it's a great start for broad risk assessment, integrating it with super high-resolution physics models will be the next big step.

Isaac Lee, Bryan Shaddy, Assad Oberai

Department of Mathematics, University of Southern California · Department of Aerospace and Mechanical Engineering, University of Southern California

cs.LG

Submitted: 2026-10-11

Updated: 2026-10-11

Comments: 18 pages, 7 figures, 1 table. Code and data: https://github.com/isaaclee2/Wildfire_Size_Flow_Matching

Code: https://github.com/isaaclee2/Wildfire_Size_Flow_Matching

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

The gist: The gist The proposed model presents a probabilistic model for predicting the temporal evolution of wildfire size using conditional generative algorithms, namely flow matching, which forecasts a time

Key concepts

Conditional Flow Matching (CFM): A generative algorithm used to create fire size predictions based on specific conditions, like weather. It works by defining a 'velocity field' that learns how to transform random noise into a realistic fire size prediction given the input conditions.
Time Series Forecasting: Instead of predicting exactly where the fire is at every point (spatial resolution), this model predicts a sequence of fire sizes over time. It forecasts how much the total acreage will change in discrete steps, making it faster for applications like risk assessment.
Autoregressive Rollout: A method used to predict future fire growth beyond the initial 3-hour step. The model uses its own previous predictions as input for the next step, simulating a 24-hour fire evolution by iteratively adding predicted growth increments.
sMAPE (Symmetric Mean Absolute Percentage Error): A metric used to measure how accurate the model's predictions are compared to real wildfire data. A low sMAPE score indicates high accuracy; the model achieved 0.39 for single steps, meaning its predictions are within a small percentage of the actual fire size.

Terminology

Flow Matching — 1× in this paper · explained in 10 episodes
Probabilistic Forecasting — 1× in this paper · explained in 3 episodes

Summary

The gist The proposed model presents a probabilistic model for predicting the temporal evolution of wildfire size using conditional generative algorithms, namely flow matching, which forecasts a time series of fire acreage rather than spatially resolved fire progression

Problem Formulation and Model Goal

The goal of this work is to predict the evolution of wildfire size based on weather, fuel, and terrain data. The model operates on a 3-hour forecasting interval where it estimates the change in fire area over that timestep based on both the current burned area and the burned area at the previous timestep. The input to the model is denoted by the vector X and consists of scalar quantities such as Current burned area and burned area obtained from the previous timestep, providing temporal context for fire growth rate, Spatially averaged 10-meter zonal and meridional wind components, Spatially averaged 2-meter relative humidity, and various terrain metrics. The full input vector has dimension |X| = 24 and the output vector has dimension |Y| = 3, where Y denotes the predicted change in wildfire area over three hours.

Conditional Flow Matching Algorithm

To generate samples from the desired conditional distribution PYX, conditional flow matching (CFM) algorithms are employed. The CFM algorithm defines a pseudo-time variable t ∈ (0, 1) and a random variable Yt which is defined as Yt = Z(1 − t) + Yt. A velocity field vt(Yt, X) is approximated using a neural network to map samples from N (0, I) to samples from PYX. The loss function minimized during training is L(vt) = 1/N Σ i vt(i), x(i) - y(i) - z(i). The velocity field is modeled using a fully connected feed-forward neural network consisting of 4 hidden layers with a width of 256, trained using the Adam optimizer.

Autoregressive Rollout and Uncertainty Quantification

For multi-step prediction, the model is applied autoregressively to simulate fire area evolution over time horizons greater than 3 hours. At each forecast step, the model receives current and previous fire area estimates alongside corresponding weather, terrain, and fuel inputs for this timestep and produces an ensemble of predicted fire area growth over a 3-hour interval. The predicted growth increment is then added to the current area used as input to obtain the fire area estimate resulting from the 3-hour growth period. Uncertainty is propagated through time using an ensemble of M = 100 realizations, where in subsequent timesteps each ensemble member is used to generate a single prediction for the next timestep in a one-to-one mapping. The result of each rollout is an ensemble of predicted fire area trajectories of the desired length.

Model Performance and Validation

The model's performance was evaluated through several metrics. For single-step predictions, the flow matching model achieved a symmetric mean absolute percentage error (sMAPE) of 0.39 relative to the reference WRF-SFIRE solutions. In recursive multi-step predictions over 24 hours for 12 held-out test cases, the flow matching model achieved a final fire area sMAPE of 0.39 while further providing meaningful quantification of forecast uncertainty. Sensitivity analysis demonstrated that the model captures physically consistent responses to variations in wind speed, temperature, and relative humidity. In single-step validation on 1,200 cases, a sMAPE of 0.39 and R2 of 0.56 were achieved. Furthermore, the Pearson correlation coefficient between the ensemble standard deviation and the absolute prediction error was found to be r = 0.64 (p < 0.001).

Data Generation Procedure

Training data is derived from wildfire spread simulations generated using WRF-SFIRE coupled with weather data from the North American Mesoscale (NAM) model. Simulations were generated for 140 wildfires occurring in the contiguous United States (CONUS) during 2023, with 12 additional simulations reserved for testing. Data augmentation involved applying 10 random rotations drawn from U(0◦, 360◦) and sampling 10 forecast times drawn from U(Tign, Tmax−∆t) for each WRF-SFIRE simulation, yielding 14,000 samples for training along with 1,200 samples for testing. Scalar inputs were derived from weather data through spatial averaging over a central 300 × 300 pixels (7.5 km × 7.5 km) of the WRF-SFIRE domain and normalized using specific transformations, such as Wind components are normalized by adding 13.5 and dividing by 27. Fire growth area was normalized using a logarithmic transformation Yˆi = ln(Yi + 1) / ln(Ymax i + 1).

Conclusion

The model is substantially more computationally efficient than spatially resolved physics-based models and machine learning surrogate models, enabling rapid generation of large ensembles at minimal cost. The scalar formulation offers practical advantages over spatially resolved wildfire spread models, particularly in terms of computational cost and compatibility with downstream applications like plume rise models. The model is suitable for risk assessment and early warning tasks where quantification of prediction uncertainty is critical. Several directions for future work include integration into early warning systems or wildfire risk assessment tools, and integration with plume rise models.

Improvements for AI systems

textbf Rewritten Probabilistic Model for Fire Size Forecasting: Using Conditional Flow Matching to Predict Time-Series Fire Acreage; The improved system can forecast a time series of fire acreage over a 3-hour interval based on current and previous fire sizes, substantially reducing computational cost compared to physics-based models.
textbf Integration with Early Warning Systems and Risk Assessment Tools; The model is directly compatible with downstream applications requiring continuous fire area estimates, such as plume rise models, enabling the computationally efficient generation of ensembles of plume rise estimates.
textbf Enhanced Uncertainty Quantification; The model provides meaningful quantification of forecast uncertainty, assessed by examining the ensemble standard deviation against the prediction error and finding a correlation coefficient of r = 0.64, which allows for better risk assessment in early warning scenarios where quantification is critical.