# Physics-Informed Surrogate Modelling in Fire Safety Engineering: A Systematic Review
## 4 Challenges and Future Directions  
The literature review of Section 2 has shown that PISM is gaining traction within FSE, but that large unexplored areas remain. Crucially, the currently best approach to incorporating physics into surrogate modelling tools is a multi-level approach whereby physical considerations are implemented from the level of the data, through the levels of the model architecture and objective functions, up to the level of inference (see Figure 9). It is strongly recommended that future studies in FSE adopt this multi-level approach from the get-go. Even when adopting a structured approach, however, PISMs frequently encounter challenges such as slow convergence rates and suboptimal minima (incomplete convergence) [41]. These difficulties stem from the added complexity of incorporating physics-based constraints into the loss function, which can create an intricate optimisation landscape. Given that one of the key advantages of surrogate modelling is computational efficiency, the added cost of physics-informed constraints must be carefully weighed against the benefits. The choice between a purely data-driven approach and a physics-informed surrogate thus depends on several factors, including the availability of training data, computational efficiency, and the necessity of enforcing physical constraints. If large, high-quality datasets are available, a data-driven model may be sufficient [29], possibly extended with cheap offline constraints for the model predictions. Conversely, when adherence to physical laws is critical, a physics-informed model remains the more reliable choice despite its computational demands. PINNs, in particular, struggle with imbalanced loss terms, as different constraints may exhibit varying convergence speeds. To address this, researchers have implemented learning rate annealing methods inspired by traditional multi-task learning [158]. Additionally, optimising the placement of collocation points--by concentrating them in regions with high residual errors--has been found to significantly improve training performance [159]. Loss reweighting strategies have also been explored, including inverse Dirichlet weighting [160], characteristic quantity-based weighting [52; 153], and meta-learning approaches that dynamically update loss functions during training [161]. Lastly, gradient-enhanced methods have shown promise in stabilising training by incorporating derivative information, particularly in high-order systems [162]. Engineering applications often involve high-dimensional and multi-scale problems, which present unique challenges for surrogate modelling [41; 163]. As the number of input parameters increases, traditional models struggle with the \"curse of dimensionality\", leading to reduced generalisation capabilities and computational inefficiencies. Additionally, in multi-scale problems, fine-scale variations can significantly influence large-scale behaviour, making accurate modelling more complex. To enhance training efficiency and overcome optimisation challenges, researchers have proposed various strategies. Adaptive activation functions offer a promising solution by aligning activation function behaviour with the underlying physics of the problem. For instance, in harmonic motion modelling, sinusoidal activation functions facilitate faster convergence by naturally capturing the system's behaviour [164]. Importance sampling techniques further improve computational efficiency by prioritising regions of the solution space where accuracy is most crucial [165]. Another key approach to improving learning efficiency is data resampling, where collocation points are adaptively sampled to correct imbalances in training data. Representative methods include the Sobol sequence [166] and Latin hypercube sampling [53]. Multi-view transfer learning has also been introduced as a technique to enhance generalisation by leveraging insights from related problems [167; 168; 169].