# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 2 Materials and Methods
### Literature Review
#### 2.1.5 Heat Transfer  
The calculation of heat transfer in FSE is governed by three modes: conduction, convection, and radiation, each described by well-established laws that can be directly incorporated into physics-informed models. The review reveals a strong focus on LCT. By directly embedding fundamental heat transfer equations into the learning process, these approaches demonstrate significant potential to overcome the computational bottlenecks and limitations associated with traditional finite element simulations in fire safety engineering. The identified models are discussed below. A summary is provided in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Article** & \begin{tabular}{c} **Output of the** \\ **Model** \\ \end{tabular} & **Model Algorithm** & \
\begin{tabular}{c} **Physics-Informed** \\ **Strategy** \\ \end{tabular} &
\begin{tabular}{c} **Implementation of the** \\ **Physics-Informed Strategy** \\ \end{tabular} \\ \hline \multirow{3}{*}{[PERSON] et al. [131]} & Splitting tensile & Partition-based & \multirow{3}{*}{FET} & Using known fracture models (prior knowledge) for feature selection \\  & strength of recycled & and & & \\  & aggregate concrete & regression-based & & \\ \hline \multirow{3}{*}{[PERSON] et al. [132]} & Tensile strength of & Partition-based & \multirow{3}{*}{FET} & Key features were determined \\  & recycled aggregate & and & & \\  & concrete & regression-based & & \\  & & & & \\ \hline \multirow{3}{*}{[PERSON] et al. [130]} & Yield strength of & Regression-based & \multirow{3}{*}{FET} & Correlation analysis, \\  & alloys & and & & \\ \cline{1-1}  & & partition-based & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physics-informed paper in the material behaviour field. In 2018, [PERSON] [133] presented an LCT neural network-based model, trained considering a loss function defined by the residuals of different governing equations (initial condition, boundary condition and partial differential equation). Similarly, [PERSON] et al. [134] presented another LCT neural network to approximate PDE solutions. Unlike traditional numerical methods, these solvers employ a mesh-free strategy, making them particularly suitable for high-dimensional heat transfer problems (many independent variables--spatial dimensions, time, and possibly other parameters like material properties). Another notable study is the one by [PERSON] et al. [135], which explores a deep learning-based approach to solving heat transfer equations involving forced and mixed convection, as well as radiation. The methodology employs a composite loss function that minimises the residuals of governing PDEs, boundary conditions, and sparse experimental temperature data. As an additional step, they also propose a method to adaptively select the location of sensors to minimise the number of temperature measurements. By leveraging automatic differentiation, the model eliminates discretisation errors, facilitating the resolution of ill-posed inverse problems, such as inferring unknown thermal boundary conditions and tracking dynamic phase interfaces. The direct incorporation of conservation laws within the loss function classifies this approach as LCT. Likewise, a temperature field solver has been proposed by [PERSON] et al., which embeds governing equations directly into the loss term definitions (i.e., LCT) [136]. A more advanced model is presented by [PERSON] et al. [14], combining LCT, ACT, and FET strategies. The loss function was constructed from the heat transfer partial differential equation (PDE) and boundary conditions. In addition, a specific configuration was adopted for the model architecture such that the grouping of neurons aligns with a well-known analytical solution. The activation functions were selected to have second-order derivatives (exponential linear unit, ELU) so that second-order derivatives would remain meaningful. Lastly, feature engineering was employed by introducing input parameters based on heat transfer principles.