PhysFire-WM: Physics-Informed Wildfire Modeling

• PhysFire-WM is a physics-informed modeling suite that integrates PDEs and neural networks to simulate wildfire propagation, fuel burn, and atmospheric interactions.
• It combines CFD-based simulators with a diffusion transformer and PINN surrogates to accurately capture fire dynamics and thermal fluxes in real-time.
• Its cross-task collaborative training (CC-Train) synchronizes infrared and fire mask predictions, significantly enhancing forecast accuracy and operational reliability.

PhysFire-WM is a suite of physics-informed, machine learning-driven models and world modeling techniques that address the prediction and simulation of wildfire propagation and its key driving processes. The PhysFire-WM framework encompasses multiple technical innovations, including the integration of partial differential equation (PDE)-based simulators into generative world models, physics-informed neural network (PINN) surrogates for coupled atmospheric-fire systems, and equilibrium moisture and smoke-tracer modules suited for operational fire-atmosphere modeling.

1. Mathematical Foundations: Governing Equations and Physical Couplings

PhysFire-WM is built upon re-implementations and augmentations of two central physical models originally found in the WRF-SFIRE and WRF-Chem frameworks:

• The nonhydrostatic, compressible Euler equations in flux form for wind and thermodynamic fields with prognostic variables,
• The two-dimensional level-set equation for fire front propagation, coupled with fuel burn ordinary differential equations (ODEs) and time-lag fuel moisture models.

The atmospheric equations can be written as a system of conservation laws (where $U, V, W$ are mass-weighted wind components, $\Theta$ is mass-weighted potential temperature, etc.): $$\begin{aligned} & \partial_t U + \nabla \cdot \bm{V} u + \mu_d \alpha \partial_x p + (\alpha/\alpha_d)\partial_\eta p \partial_x \phi = F_U \ & \partial_t \Theta + \nabla \cdot \bm{V} \theta_m = F_\Theta \ & \text{Other equations for mass, geopotential, and moisture species.} \end{aligned}$$ The fire front is described by the evolution of a level set $\psi(t,x,y)$: $\partial_t \psi + S(x,y,t)\|\nabla \psi\| = 0,$ with $S$ specified by a modified Rothermel rate: $S = R_0(1+\phi_W+\phi_S),$ where $\phi_W$ and $\phi_S$ account for wind and slope effects, and $R_0$ is the canonical spread rate.

Burned fuel at location $(x,y)$ decays exponentially after ignition time $t_i(x,y)$ according to

$\frac{dF}{dt} = -\frac{F}{T_f}, \quad F(t_i)=1$

and the corresponding energy fluxes are transferred to the atmospheric fields.

The equilibrium time-lag moisture model governs $m_k$, the moisture content of fuel class $k$, via

$$\frac{dm_k}{dt} = \begin{cases} \frac{E_d - m_k}{T_k}, & m_k > E_d \ 0, & E_w \leq m_k \leq E_d \ \frac{E_w - m_k}{T_k}, & m_k < E_w \end{cases}$$

with rain-driven effects handled by a saturation regime and ODE step discretization.

2. Physics-Informed World Modeling and Surrogate Training

PhysFire-WM advances wildfire prediction by embedding physics-based constraints and priors into world model (WM) architectures. The framework marries a diffusion-transformer video generator with structured priors extracted from a PDE fire simulator—designated as the "Physical Simulator $P_\phi$"—conditional on environmental state ($\mathcal{E} = \{$terrain, wind, fuel$\}$) and historical infrared fire masks. The resulting model architecture comprises three synergistic components:

• Physical Simulator ($P_\phi$): Numerically solves the thermal balance PDE

$$c\frac{\partial T}{\partial t} = \nabla \cdot (k\nabla T) - (\bm{v} + \gamma \nabla z) \cdot \nabla T + S(T)$$

where the source term $S(T)$ is determined by local combustion and loss dynamics. This prior is discretized and parameter-fitted directly to observed thermal fields.

• Multimodal Tokenizer ($E_\eta$): Projects infrared video $V_\mathrm{FireIR}$, prior masks $V_\mathrm{PriorMask}$, and associated prompts/control masks into unified spatiotemporal embedding streams $cTokens$, with mask controls dictating reconstruction and preservation regimes across temporal segments.
• Diffusion Transformer ($G_\psi$): Implements a multi-stage denoising transformer operating over video latents, trained by a continuous-time flow-matching loss:

$$L_\mathrm{DiT} = \mathbb{E}\left\| u_\theta(x_n, cTokens, n) - (x_1-x_0) \right\|^2, \quad x_n = n x_1 + (1-n)x_0$$

Systematically, the physics-informed prior masks enter cross-attention layers, constraining and informing the generative process to remain aligned with physically plausible behaviors.

Enforcing Physics Consistency

PhysFire-WM couples explicit prompt-based enforcement—with initial frames locked to empirical IR and following frames conditioned on PDE-generated priors—and implicit cross-attention at every transformer block. The system thereby both restricts dynamics to the phase-space permitted by the governing equations and regularizes per-frame diffusion updates to consistently reflect combustion and heat transfer.

3. Cross-Task Collaborative Training (CC-Train)

A central innovation in PhysFire-WM is joint prediction and gradient coordination across heterogeneous task domains:

• Infrared Field Prediction: Generates future IR frames directly.
• Fire Mask Prediction: Predicts spatially explicit, binary fire boundaries.

The CC-Train strategy leverages parameter sharing in $E_\eta$ and $G_\psi$, with only prompt embeddings varying by output stream. Simultaneous computation of thermal denoising loss ($L_\mathrm{IR}$) and binary cross-entropy mask loss ($L_\mathrm{mask}$) enables bidirectional regularization where precise boundary estimation constrains thermal diffusion, and physically consistent heat fields sharpen spatial delineation. The aggregate loss is

$$L_\mathrm{total} = L_\mathrm{IR} + \lambda L_\mathrm{mask}$$

with $\lambda$ set empirically. Ablation studies demonstrate that both physics priors and cross-stream training yield significant improvements in area under precision-recall (AUPRC), PSNR, F1, IoU, and other metrics (Zhou et al., 19 Dec 2025).

4. Implementation Pipeline and Deployment

PhysFire-WM combines modern machine learning tools and specialized numerical simulation environments. Key components and workflow stages include:

• Simulator and PINN Surrogate Toolkit: Core physical models (WRF-SFIRE or its re-implementation) are defined via Julia’s DifferentialEquations.jl and ModelingToolkit.jl, with PINN surrogates constructed using NeuralPDE.jl (Flux and GalacticOptim backends) (Bottero et al., 2020). Target variables are approximated by feed-forward networks with tanh activations, and all derivatives are computed via automatic differentiation (AD).
• Training Protocol: Parameter-efficient fine-tuning (LoRA, rank=128) is performed on GPU (NVIDIA RTX A6000) for 50 epochs, with AdamW optimizer at LR=$10^{-4}$, batch size 4, yielding convergence on both synthetic and real wildfire drone video datasets (Zhou et al., 19 Dec 2025). PINN-based training (CPU-based, 2-5k iterations) benefits from warm-starting—parameters from prior runs reduce iteration count by 2–5$\times$.
• Data and Preprocessing: Static terrain/fuel data are sourced from NCAR, LANDFIRE, and high-res DEMs; environmental inputs include GFS wind and boundary conditions. Joint spatial and temporal co-registration is a prerequisite for model fidelity.
• Deployment and Real-Time Execution: For operational use, a typical workflow involves forecast ingestion, terrain smoothing, PINN system reconfiguration, retraining or updating the surrogate, and extraction of fireline contours (zero-level sets of $\psi$) for display in GIS. Turnaround for real-time updating is 2–3 minutes on 8-core CPUs for PINN surrogates, and tens of seconds per batch for the world model (Bottero et al., 2020).
• Moisture and Smoke Module Configuration: WRF/WRF-Fire/WRF-Chem operationalization requires appropriate compilation/configuration flags, consistent timescales across modules, WRF namelists enabling fire and moisture coupling, and proper input field preparation (Kochanski et al., 2012).

5. Validation, Benchmarking, and Results

PhysFire-WM has been validated in both idealized synthetic and real-wildfire domains:

• The PINN-based solver matches traditional WRF-SFIRE fireline predictions to within 3–5% directed Hausdorff error (synthetic/Isom Creek test cases), and yields speedups of 10$\times$ in simulation time (train+predict: 4–10 minutes CPU vs. 1–3 hours for traditional solver) (Bottero et al., 2020).
• The physics-informed world model achieves AUPRC=0.89 (mask, +6.8% vs. best baseline), IoU=0.89, F1=0.94, MSE=0.01, and IR PSNR=23.62 dB, SSIM=0.80, LPIPS=0.09, FVD=0.001 (single-region). Cross-region generalization is strong (AUPRC=0.83, PSNR=23.26) (Zhou et al., 19 Dec 2025).
• Ablations confirm that omitting physics priors degrades mask AUPRC (from 0.85 → 0.82) and PSNR (from 23.00 → 22.76), whereas removing CC-Train yields substantial decreases in both modalities (Zhou et al., 19 Dec 2025).
• The equilibrium time-lag moisture model, calibrated using Canadian reference parameters, accurately tracks hourly to daily fuel moisture response to both atmospheric drying/wetting and rain events, matching observational curves and supporting smoke emission/advection studies (Kochanski et al., 2012).

6. Limitations and Current Research Trajectories

PhysFire-WM, while demonstrably effective, faces several recognized limitations:

• Full GPU/multithread training for PINNs in NeuralPDE.jl is under development, temporarily limiting scalability for large geographies.
• Fuel maps must currently be smooth representations rather than raw grid matrices (NeuralPDE Issue #177), constraining spatial heterogeneity modeling.
• Stability concerns exist for PINN surrogates on very large domains; further work on domain normalization/scaling is ongoing.
• Efforts are active in 3D coupled Euler-fire PINN, introduction of CNN/RNN layers for handling high-resolution field inputs, and extension of smoke modules beyond passive tracer assumption.
• Planned FEPS-based emission modules for PM2.5/CO2 species, and full chemistry-gas-phase integration, are in development for WRF-Chem compatibility (Kochanski et al., 2012).

7. Applications and Future Prospects

PhysFire-WM underpins continuous-time, physically plausible forecasting for real-time wildfire management and for retrospective reconstruction (forensic analysis) of ignition/spread scenarios (Bottero et al., 2020, Zhou et al., 19 Dec 2025). By fusing the strengths of physics-based simulation, machine-learned surrogates, and multimodal world modeling, it provides actionable predictions of both fire advance and thermal intensity. This unification supports decision-making in containment planning and contributes foundational advances for broader disaster forecasting systems. The explicit encoding of physical laws in generative architectures marks a demonstrable advance in the operational reliability of datacentric, AI-driven simulation pipelines.