# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 2 Materials and Methods
### Literature Review
#### 2.1.3 Structural Fire Engineering  
In the field of structural fire engineering, several studies have used the data-driven approach. These include models trained to predict the thermo-structural response of timber \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. [85] & Fire spread map & Neural-network based & LCT & Loss terms for residual PDE and initial condition, and boundary condition were included in the total loss calculation for model training. \\ \hline [PERSON] et al. [87; 88] & Spatiotemporal evolution of fire & Regression-based (ROM, DEIM) & ACT & Mathematically reduced form for solving a complex system \\ \hline [PERSON] et al. [86] & Spatiotemporal evolution of fire, wind velocity and heat transfer coefficient & Neural-network-based & LCT & A loss function was adopted that penalises deviations from the governing PDEs \\ \hline [PERSON] et al. [84] & Wildfire risk score & Neural-network-based & ACT & The physics-embedded entropy layer uses the Boltzmann–Gibbs entropy equation from statistical mechanics, enabling the architecture to inherently compute a physically meaningful quantity \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physics-informed models in the wildfire field. elements, the fire resistance of compressed steel members, composite shallow floor systems, timber columns, gypsum plasterboard walls, cold-formed steel walls, concrete-filled steel tube columns, and concrete beams and columns [89; 90; 91; 92; 93; 94]. In addition, several PISM/PIML studies were identified as part of the literature review, as presented in Table 3. [PERSON] et al. [95] used a combination of engineering knowledge, understanding of fire behaviour, and data availability to select the most relevant input features, thus adopting a FET approach to predict the fire resistance of timber columns. Similarly, [PERSON] et al. used FET to predict reinforced concrete column fire resistance [96]. Prior to training the ML model, the authors performed frequency and correlation analyses, identifying influential features based on correlation strength. They also compared their findings to existing formulas. This multi-faceted approach narrowed the feature space to parameters with the strongest statistical relationship to fire resistance. [PERSON] et al. developed a model to predict the fire resistance of concrete-encased steel columns [97], adopting both FET and OCT. First, an ANN predicts the equivalent temperatures of the column's components (steel, concrete, rebar). Features were selected based on a parametric study, a form of FET. Subsequently, to translate these predicted temperatures into fire resistance capacity, they used established engineering relationships between temperature and material strength, i.e., OCT. This offline step acts as a physical link, incorporating domain knowledge without directly influencing the ANN's training. Thus, while the ANN itself is purely data-driven, the overall surrogate model integrates physics through feature engineering and an offline physical constraint, effectively separating the thermal and mechanical aspects of the problem. A similar approach to OCT was presented by [PERSON] et al., who trained an ANN to predict the equivalent temperature of the steel section for concrete-encased steel composite columns [97]. By implementing the obtained steel temperature in a physical (finite element) model, the final result for the column capacity can be considered an application of OCT.  
LCT has also gained significant attention in this field. [PERSON] et al. embedded the Euler-Bernoulli beam theory and [PERSON]'s principle in the loss function when training a model to predict the structural response of functionally graded beams [98], and [PERSON] et al. proposed a neural network to solve coupled thermo-mechanical problems of functionally graded materials [99].