This work focuses on estimating the state of health of complex industrial systems using sensor data collected over time to monitor such systems, while taking into account the physics governing their operation. We focus on probabilistic estimation for learning health indicators that can provide a continuous estimate, ideally in real time, of the state of health of the system, moving from a functional state to a possibly degraded state, while being able to integrate a set of intermediate states. By taking into account the physics governing the system under study, invariant characteristics can be combined with information learned from measured/observed data. The aim of this hybridation is to quantify and limit the uncertainty associated with estimating health indicators over the life cycle of the real system. The construction of such system health indicators via the proposed modelling should be able to highlight, via statistical properties in terms of the capacity to detect variables or co-variables relevant to the prediction, the relevance of considering pre-constructed indicators separately or via a ‘combination’ and or a ‘selection’ of subsets of them, depending on the final relevance to the indication of the state of health of the system studied.