# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 2 Materials and Methods
### Literature Review  
#### 2.1.1 Fire Dynamics  
Fire dynamics simulations require solving physical equations specifying the conservation of mass, momentum, and energy. High-fidelity approaches, such as computational fluid dynamics (CFD), offer detailed predictions but demand significant computing power and long simulation times [54; 55].  
Several data-driven machine learning models in the sub-discipline of fire dynamics were identified, most of which make predictions based purely on training data without explicit integration of physical laws. [PERSON] et al., for example, developed an ML model trained on CFD-generated fire simulations, making it a fully data-driven approach [56]. Other studies developed flashover prediction models, relying on sensor data for learning temporal patterns, without embedding governing fire dynamics. Applied methodologies included long short-term memory (LSTM) networks [57], support vector regression (SVR) [58], and conditional generative adversarial networks (GANs) [59].  
As part of the review in the subfield of fire dynamics, PIML studies were identified. FlashNet and xFlashNet are considered as FET [60; 61]. The use of maximum operating temperatures of heat detectors is a form of a physical constraint, based on physical limitations, and was considered in this research on the data in the preprocessing phase. To have a more physical model, they used the operational limit of the detectors to cut the data. The integration of this soft constraint can be considered part of the FET strategy [61]. Subsequently, they utilise graph neural networks (GNNs) to capture spatial-temporal fire dynamics [61] to predict flashover within the next 30 s, using data from the CFAST simulator for temperature history at the location of heat detectors.  
[PERSON] et al.'s reduced-order modelling (ROM) approach projects governing CFD equations into a reduced-dimensional space, preserving fire physics while significantly improving computational efficiency [62]. The results of 220 FDS simulations were used to extract dominant spatial features using proper orthogonal decomposition to replace the full-order model with a small system of ordinary differential equations (ODEs) that can effectively reduce the computational cost while maintaining physics. Subsequently, a fully data-driven neural network-based model (in this case, a full field spatial distribution CNN) was trained to capture the relationship between input (geometry and fire size) and output fire dynamics (temperature and velocity fields). Since the physical link is laid before the model and is not included within the ML; this method is categorised as FET.  
Similarly, surrogate modelling with ANN and multiple linear regression (MLR) has been used to specify fire source properties for CFD simulations [63]. Where this combination of a data-driven surrogate and a physical model together acts as a surrogate for a more expensive physical model, the joint surrogate modelling approach can be classified as offline-constrained. In other words, the final calculation step applying a physical model effectively constrains the surrogate model output to physically relevant solutions (as controlled by the physics of the physical model).  
Despite these developments, several methodological limitations are apparent. While [61] presents some performance comparisons, they are restricted to accuracy metrics and omit evaluations of physical constraint violations. No standard criteria exist to assess whether predictions adhere to conservation laws or boundary conditions.  
Table 1 summarises the identified PISM applications in fire dynamics, listing their model algorithm and the physics-informed techniques used. PIML remains relatively underexplored in this domain, with only a few studies using feature engineering or offline  
constraints. No studies applying loss-constrained techniques were found, and none explicitly incorporate architectural constraints--both of which offer promising directions for improving model reliability.