Conserving cultural heritage involves modeling complex physical processes, including time-dependent behaviors. In this contribution, we present a digital framework that integrates Scientific Machine Learning techniques with classical numerical methods to support cultural asset analysis and predictive maintenance [1]. The architecture combines Physics-Informed Neural Networks (PINNs) and Reduced Order Models (ROMs) to solve parametrized partial differential equations, addressing both direct and inverse problems computationally efficiently [2, 3]. The framework exploits sensor data and digital replicas of heritage elements to inform simulations and model updates. PINNs incorporate physical constraints into learning algorithms, while ROM techniques enable fast approximations in high-dimensional scenarios, especially when full knowledge of system parameters is unavailable. Particular attention is given to the coupling of data-driven and physics-based components and the challenges of generalization, sampling, and model reliability in multi-scale settings [4]. This contribution explores how hybrid modeling strategies, combining physics-informed neural networks and reduced order models, can be effectively employed within a structured digital workflow to conserve cultural heritage. Through simulated scenarios involving parameterized time-dependent PDEs, we assess the potential of such techniques to support efficient, physics-consistent approximations, furnishing reliable and computationally accessible tools supporting decision-making in the cultural heritage field. REFERENCES [1] A. Quarteroni, P. Gervasio, F. Regazzoni, Combining physics-based and data-driven models: advancing the frontiers of research with scientific machine learning. Math. Models Methods Appl. Sci.. [2] M. Raissi, P. Perdikaris, and G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys (2019). [3] J. S. Hesthaven, G. Rozza andB.Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer. (2024). [4] C. Valentino, G. Pagano, D. Conte, B. Paternoster, F. Colace, M. Casillo, Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model. Math. Comput. Simul. (2025).