This work aims to advance the optimisation of the efficiency of thermal installations in buildings, contributing to the achievement of Zero Energy Buildings (ZEB) in the context of maintenance and operation. This is achieved through an innovative proposal that merges machine learning techniques with thermoeconomics to perform diagnoses in building thermal systems and identify cost overruns generated by intrinsic anomalies in the components and quantify their induced effects on the rest of the components. To date, the few contributions combining these techniques have been limited to industrial applications and cost calculation, without addressing their application to building thermal systems, both from a dynamic perspective and for maintenance purposes. Research using Physics-Informed Neural Networks, PINNs, in this area is even scarcer, which underlines the complexity of defining a suitable methodology. Thus, the proposal integrates PINNs with a thermoeconomic diagnosis based on characteristic curves, allowing the comparison of the current operating condition with an anomaly-free reference condition to assess the existence of anomalies and their effects. For this reason, reference models are generated for the first time with PINNs, which represents a break with the conventional maintenance approaches used by professionals in the sector. Therefore, this methodology incorporates techniques that require specialised knowledge in thermodynamic and informatics areas, which motivates the present work to be focused on the exhaustive description of the methodology and to highlight the importance of continuing to explore lines of research in this unexplored field.