# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 2 Materials and Methods
### Literature Review
#### 2.1.4 Material Behaviour  
Data-driven ML techniques have been widely used to estimate material behaviour under ambient conditions [103; 104; 105; 106; 107]. However, at elevated temperatures, additional degradation mechanisms come into play, complicating predictive modelling due to the nonlinear and irreversible nature of material degradation. Therefore, machine learning has also been extensively applied to assess the performance of materials subjected to high temperatures. Data-driven approaches have been used to evaluate ceramics [108], stainless steel [109; 110; 111], concrete [112; 113; 114; 115; 116; 117; 118], and fibre-reinforced concrete [119; 120; 121; 122; 123]. A subfield of material behaviour at high temperatures that has used ML extensively is fire-induced spalling, which refers to the detachment and ejection of concrete fragments when exposed to extreme heat [124]. This phenomenon results from a highly complex interaction of thermal, mechanical, hygral, and chemical processes, making it challenging to develop a unified predictive framework. Despite extensive research, no single dominant mechanism has been universally identified, largely due to the interdependencies among these processes [125]. Data-driven models for predicting fire-induced spalling have been proposed leveraging large experimental datasets to identify correlations among key factors such as concrete composition, moisture content, heating rate, and applied stress. The \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. [95] & Fire resistance of timber columns & Regression-based, partition-based, neural-network-based & FET & Features were selected through data processing and prior knowledge \\ \hline [PERSON] et al. [100] & Thermomechanical & Neural-network based & LCT, ACT & Embedded physics in loss functions with different networks for different physics. \\ \hline [PERSON] et al. [102] & Thermomechanical & Neural-network based & LCT, ACT & A mixed PINN architecture for coupled thermo-mechanical analysis, together with physical loss functions, is used. \\ \hline [PERSON] et al. [97] & Fire resistance of the composite column & Neural-network based & FET & Frequency analysis used for feature selection \\ \hline [PERSON] et al. [101] & Fire resistance of the reinforced concrete column & Regression-based (Causal analysis) & ACT & Modifying links between parameters based on prior knowledge and causal analysis \\ \hline [PERSON] et al. [99] & Thermomechanical & Neural-network based & LCT & Loss functions created to incorporate the thermo-elastic partial differential equation with the degradation of the material \\ \hline [PERSON] et al. [96] & Fire resistance of the concrete column & Regression-based & FET & Frequency analysis, correlation analysis \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physics-informed models in the structural behaviour field. adopted approaches include ANN, SVM, and DT [24; 126; 127; 128; 129]. [PERSON] et al. demonstrated that specimen size significantly influences pore pressure buildup and stress distribution, leading to inconsistencies when scaling results across datasets [128]. As a result, purely data-driven ML models may struggle to generalise across varying conditions. The application of physics-informed strategies in high-temperature material modelling remains limited. All identified cases [130; 131; 132] adopt FET, see Table 4. Specifically, [PERSON] et al. proposed a model capable of predicting the properties of alloys at high temperatures [130]. They translated the raw data taken from the experiment into \"synthetic alloy features\". This involved computing crucial microstructure-related properties, such as the volume fractions of key phases and phase transformation temperatures, which directly influence alloy strength.