# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 1 Introduction: Addressing Challenges in Fire Safety Engineering with Surrogate Modelling
### Surrogate Modelling Algorithms  
Surrogate modelling algorithms can be broadly categorised into regression-based, neural network-based and partition-based categories (see Figure 2) [23]. Regression-based approaches are widely used due to their interpretability [24; 25]. These methods establish explicit mathematical relationships between input variables and outputs, with the simplest form being polynomial regression. Linear regression (first-order polynomial) is particularly popular due to its simplicity and minimal computational cost. However, for highly nonlinear systems, higher-order polynomial models may be necessary to capture complex input-output relationships. While increasing the polynomial order can enhance accuracy, it also raises the risk of overfitting, where the model performs well on training data but fails to generalise to other data points within the intended parameter space. Regularisation techniques, by adding a penalty for model complexity, can mitigate this issue [26]. Additionally, support vector machines (SVMs), though originally developed for classification, can be employed in surrogate modelling through support vector regression (SVR), offering robustness and flexibility in capturing nonlinear relationships [27].  
Figure 1: Surrogate modelling in fire safety engineering (FSE).  
For systems with highly complex and nonlinear behaviours, neural network-based models provide a more flexible alternative [28]. A neural network consists of a single or multiple layers of interconnected neurons, each applying an activation function to transform inputs into outputs [29]. The neural network's reported flexibility then results from the use of nonlinear activation functions in a system with multiple interconnected layers. This allows them to learn intricate mappings between inputs and outputs, and approximate a wider range of complex functional forms compared to traditional regression models with fixed basis functions. However, the complex interactions within the multiple layers and the large number of learnable parameters limit interpretability, resulting in the neural network's 'black-box' nature. Furthermore, large datasets are required to effectively train the high number of parameters within a multi-layer model and avoid overfitting, especially when dealing with complex, high-dimensional problems [30]. The most widely used neural-network-based surrogate modelling approaches are artificial neural networks (ANNs), convolutional neural networks (CNNs), and long short-term memory (LSTM) networks. ANNs are general-purpose models composed of layers of neurons that process information through weighted connections and activation functions, enabling them to approximate complex relationships in data. CNNs, a specialised type of ANN, are particularly effective for spatially structured data, utilising convolutional layers to extract hierarchical features, making them widely used in image and pattern recognition tasks. LSTMs, a class of recurrent neural networks (RNNs), are designed to handle sequential data by maintaining memory over time through specialised gating mechanisms, making them well-suited for time-series forecasting and dynamic system modelling.  
Decision-tree-based models are another main category of surrogate modelling. This category relies on the identification of separated subcategories for the data [31]. They are effective when the data can be separated into subcategories, each with a different behaviour and thus a different model. The basic model uses a tree-like structure to categorise based on input features [32]. Example approaches within this category are random forest (RF) [33], gradient boosting machines (GBMs) [34], and extreme gradient boosting algorithm (XGBoost) [35].