Physics-informed neural networks for parameter learning of wildfire spreading

TL;DR

This work introduces a physics-informed neural network (PiNN) designed to learn the unknown parameters of an interpretable wildfire spreading model that will enhance intelligent wildfire management and risk assessment, providing a powerful tool for proactive and reactive strategies.

Abstract

Wildland fires pose a terrifying natural hazard, underscoring the urgent need to develop data-driven and physics-informed digital twins for wildfire prevention, monitoring, intervention, and response. In this direction of research, this work introduces a physics-informed neural network (PiNN) designed to learn the unknown parameters of an interpretable wildfire spreading model. The considered modeling approach integrates fundamental physical laws articulated by key model parameters essential for capturing the complex behavior of wildfires. The proposed machine learning framework leverages the theory of artificial neural networks with the physical constraints governing wildfire dynamics, including the first principles of mass and energy conservation. Training of the PiNN for physics-informed parameter identification is realized using synthetic data on the spatiotemporal evolution of one- and two-dimensional firefronts, derived from a high-fidelity simulator, as well as empirical data (ground surface thermal images) from the Troy Fire that occurred on June 19, 2002, in California. The parameter learning results demonstrate the predictive ability of the proposed PiNN in uncovering the unknown coefficients of the wildfire model in one- and two-dimensional fire spreading scenarios as well as the Troy Fire. Additionally, this methodology exhibits robustness by identifying the same parameters even in the presence of noisy data. By integrating this PiNN approach into a comprehensive framework, the envisioned physics-informed digital twin will enhance intelligent wildfire management and risk assessment, providing a powerful tool for proactive and reactive strategies.

Figures (14)

• Figure 1: Architecture of the proposed PiNN for learning the parameters of the wildfire spreading model. The ANN on the left represents the physics-uninformed (data-driven) surrogate predictor, while the right network illustrates the physics-informed (data-uninformed though) residual, initial and boundary conditions of the wildfire model, and the data-informed cost function (data fitting) that penalizes deviation of the surrogate model predictions from the synthetic data.
• Figure 2: Parameter learning and convergence in the 1D firefront of the wildfire spreading model. The predicted vector of the three model parameters is $\hat{\bm{\theta}} = \left[0.408\,\, 0.25\,\, 0.61\right]^\mathsf{T}$, while the true vector used for generating the training dataset is $\bm{\theta}^{*} = \left[0.41\,\, 0.25\,\, 0.61\right]^\mathsf{T}$.
• Figure 3: 1D spatiotemporal firefront for the three state variables: $T, E, X$. The left column presents the explicit solution of the physics-based wildfire spreading model, while the right column displays the prediction of PINNs. Both cases are provided in a dimensionless form.
• Figure 4: Comparison of the temperature distribution between the explicit solution and the prediction of PiNNs at two specific non-dimensional time instants: $t = 0.5$ and $t =1$, for all nodes across the spatial firefront.
• Figure 5: Representation of the training dataset distributions across the temperature profile in both space and time for Case 1 (optimal), 1A, 1B, and 1C. Dot symbols represent the sampling data points used for training in each case.