# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 2 Materials and Methods
### Literature Review
#### 2.1.2 Wildfire  
Wildfire behaviour is a highly complex phenomenon influenced by multiple interrelated factors, including ignition sources, fuel composition, weather conditions, and topography [64; 65]. While physics-based models offer detailed simulations, their high computational costs often limit real-time applications. In contrast, advances in remote sensing and ML have enabled the development of data-driven approaches for wildfire monitoring, detection, and prediction [66; 67; 68]. One key application of ML in wildfire research is fuel characterisation, where large datasets from satellite imagery are analysed to classify vegetation types and assess fire risk [69; 70]. These models predominantly rely on partition-based models, which are well-suited for classification tasks. Similarly, for wildfire detection, ML algorithms process vast amounts of satellite and sensor data to identify active fires in near real-time [71; 72]. Neural network-based and decision partition-based models are widely used in this domain [73; 74; 75; 76]. Techniques such as learning without forgetting allow models to retain previously learned features while adapting to new datasets. However, these methods operate purely within a statistical learning framework and do not explicitly incorporate fire physics [77; 78]. Another critical application is wildfire spread prediction, where ML models aim to forecast fire progression over time. Data-driven models, such as CNNs, have been used to predict fire spread dynamics through autoregressive processes that stream data from live satellite feeds [79; 80; 81; 82]. These models learn spatio-temporal patterns from past wildfire simulations but do not enforce physical constraints in their architecture or training. Recent research has explored integrating constraints in preprocessing. [PERSON] et al. introduced a neural network-based model trained on WRF-SFIRE simulations [83]. A preprocessing step transforms simulated fire arrival time data to mimic satellite measurements; however, this does not constitute FET, as no physical considerations underlie the feature specification. Building on this trajectory, a recent study proposed embedding a physics-based entropy formulation from statistical mechanics directly into the architecture of a neural network, enabling interpretable wildfire risk predictions grounded in physical principles [84]. By designing a custom entropy layer as part of the model's structure, the authors adopted an \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Article** & **Output of the Model** & **Model Algorithm** & **Physics-Informed Strategy** & **Implementation of the Physics-Informed Strategy** \\ \hline [PERSON] et al. [61] & Flashover time & Neural network-based & FET & Using a soft constraint on the data by introducing a temperature cut-off to take into consideration the working temperature limit for detectors. \\ \hline [PERSON] et al. [62] & Temperature, velocity fields & Neural network based on CNN & FET & Using ROM as a physical link before on data to reduce the complexity of the problem and keeping the physics at the same time. \\ \hline [PERSON] et al. [63] & Temperature fields, flow fields...(CFD output) & ANN & OCT & A two-step calculation is performed whereby fire source properties generated by a data-driven model are implemented in a physical (CFD) calculation. \\ \hline [PERSON] et al. [60] & Flashover time & Neural network-based & FET & Using a soft constraint on the data by introducing a temperature cut-off to take into consideration the working temperature limit for detectors. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physics-informed models in fire simulation. architecture-constrained technique that aligns model outputs with theoretical understandings of landscape complexity and fire susceptibility. In contrast to the above data-driven approaches, physics-informed studies have been gaining some traction. Table 2 provides an overview of the identified studies. In this regard, [PERSON] et al.