# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 1 Introduction: Addressing Challenges in Fire Safety Engineering with Surrogate Modelling
### Strategies for Implementing Physics in Surrogate Models  
Different strategies exist for making physics-informed models, and a classification system for physics-integration strategies for PIML has been presented in [49; 50]. The following strategies have been identified (visually represented in Figure 4):  
Figure 3: Comparing data-driven models and physics-informed models.  
* **Loss-constrained technique (LCT)**: These models integrate physical knowledge by introducing physical constraints directly into the training process through the loss function. This is typically achieved by incorporating penalty terms that quantify the violation of known physical laws (e.g., conservation of mass, momentum, and energy, or governing partial differential equations). During training, the model is penalised for making predictions that do not satisfy these constraints. While this approach encourages the model to learn physically consistent solutions, it does not entirely prevent the possibility of non-physical predictions, especially in regions with limited data or complex physics. The strength of the penalty term influences the degree to which the model adheres to the physical constraints.
* **Architecture-constrained technique (ACT)**: This strategy involves embedding physical laws directly into the architecture of the surrogate model. This can be done by designing specific activation functions, network layers, or even entire model structures that inherently respect or align with fundamental physical properties or concepts. As an example, suppose we are modelling the cooling of a steel section at uniform temperature after fire exposure. To ensure that the model respects the basic physics of cooling (i.e., the temperature must decay over time and never increase after the heat source is removed), we could design the model architecture to enforce this by using exponentially decaying functions (e.g., \(T(t)=Tambient+(T_{initial}-Tambient)\cdot e^{-\lambda t}\)) as part of the output layer. This guarantees that predicted temperatures always decay monotonically over time, reflecting the natural cooling behaviour of materials post-fire. This approach offers a strong form of physics integration, as it makes predictions that violate the implemented physical laws mathematically impossible. However, designing such architectures can be complex.
* **Offline-constrained technique (OCT)**: These models apply physical constraints after the surrogate model has been trained, refining predictions during the inference phase. One approach is to perform a \"sanity check\" to ensure the model's output falls within physically plausible ranges or adheres to basic physical principles. Another effective strategy involves using the initial output from the trained model as an input to a separate, well-established physical correlation or a set of physical equations. This allows for the imposition of more complex physical relationships on the model's predictions, generating a new, physically refined output. This, in other words, introduces a physically informed refinement as an additional final step in the predictions by the trained model. This latter approach closely links with the ACT approach to PISM: the architecture of the global surrogate model is split into a data-driven model and a physical model, whereby the former provides input to the latter.
* **Feature engineering technique (FET)**: The variables describing the training data are engineered to align with physical insights, such as non-dimensional parameters. This avoids, for example, non-physical combined effects of parameters within the trained model. This is thus a strategy for incorporating physics in the preprocessing stage.  
It is necessary to highlight that using a combination of strategies is possible. These strategies and their combinations offer varying balances between flexibility and physical consistency in surrogate modelling.