Predicting protected steel temperatures in fire using physics-informed surrogate models

Surrogate models offer efficient alternatives to computationally intensive fire simulations.This study evaluates linear and sigmoid-based regression models for predicting the maximum temperature of fire-protected steel elements exposed to physically-based fires.The focus lies on enforcing physical realism through a constrained sigmoid output and a penaltybased loss function targeting conservative predictions.Results demonstrate that while the linear regression model achieves fast and accurate performance with large datasets, the sigmoid model inherently respects physical constraints and offers robust predictions also under limited data. INTRODUCTIONAccurate prediction of steel temperatures during fire exposure is essential for ensuring structural safety and assessing the fire resistance of buildings [1,2].While detailed numerical models based on physically-based (parametric) fire curves and thermal calculations can provide reliable estimates, their high computational cost makes them impractical for routine design checks, sensitivity analysis, or probabilistic methods.Surrogate models offer a more efficient alternative by approximating complex simulations with simplified, faster-running models.These techniques have been widely used in other engineering fields, including aerodynamics, heat transfer, and materials science, where they reduce computational effort without compromising predictive capability [3][4][5].Methods such as Kriging [6,7], polynomial chaos expansions [8,9], and neural networks [10] are wellestablished, but their adoption in structural fire engineering has been limited.Moreover, conventional surrogate models often produce unrealistic or non-physical outputs when applied outside the training domain [11].To overcome these limitations, physics-informed surrogate models (PISMs) incorporate physical laws and engineering constraints into the modelling process.This approach has shown promise in improving accuracy, consistency, and generalization, particularly in scenarios with limited training data or strong physical dependencies [12].In structural fire applications,