# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 5 Conclusions  
This study systematically reviewed the state-of-the-art of PISMs in FSE. By embedding fundamental physical principles--such as conservation laws, heat transfer equations, and material degradation mechanisms--into machine learning frameworks, PISMs improve predictive accuracy, interpretability, and reliability. Case studies spanning fire dynamics, wildfire, structural fire engineering, material behaviour, and heat transfer illustrate the diverse applications and advantages of this methodology. Four distinct strategies for integrating physics into machine learning models have been identified:  
* Feature Engineering Technique (FET): Incorporates physics-based variables and transformations into the dataset before training. * Loss-Constrained Technique (LCT): Embeds physics-based constraints directly into the loss function to guide optimisation. * Architecture-Constrained Technique (ACT): Modifies the neural network structure to enforce physical constraints (e.g., sub-models, and activation functions for bounded outputs). * Offline-Constrained Technique (OCT): Applies physics-based corrections in post-processing, refining model predictions after training. Each approach presents trade-offs between accuracy, computational cost, and physical fidelity. It is important to recognise that different techniques incorporate physics to varying degrees. When carefully designed, architectural constrained techniques (ACTs) and loss-constrained techniques (LCTs) can strictly enforce certain physical laws, ensuring that model outputs remain consistent with the governing physics. Combining multiple strategies often leads to better performance and greater efficiency than relying on a single method. To systematically integrate these techniques, a stepwise framework for building PISM is proposed. This framework outlines how and when each method can be introduced during the modelling process to enhance both physical realism and computational performance. Despite these advancements, challenges remain. PISMs often face convergence difficulties, particularly under highly nonlinear conditions (such as fire), and many studies overlook critical aspects such as uncertainty quantification, data efficiency, and multi-physics integration. Future research should focus on addressing these limitations and developing standardised validation metrics to enhance model credibility. Open-source frameworks will also be crucial in promoting wider adoption and refinement of PIML techniques. Ultimately, the choice between purely data-driven and physics-informed approaches depends on data availability, computational constraints, and the risks associated with unphysical predictions. In safety-critical applications such as fire engineering, where physically inconsistent predictions can have severe consequences, physics-informed models are indispensable. By refining physics integration techniques and expanding their application, researchers and engineers can develop more reliable and actionable predictive tools for fire safety optimisation, risk assessment, and design. Conceptualization, R.Y. and R.V.C. ; methodology, R.Y., R.V.C. and F.P. ; formal analysis, R.Y. ; investigation, R.Y. ; writing--original draft preparation R.Y. ; writing--review and editing, F.P. and R.V.C. ; visualization, R.Y. ; supervision, R.V.C. ; funding acquisition, R.V.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the European Union grant number 101075556 (ERC, AFireTest). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.