We decided in 2018 to test the Batisense solution, a prediction solution developed by the Probayes company, that schematizes the building as a set of electrical/thermal circuits in order to model its behavior. From an operational point of view, using a model from the cloud to manage distribution on the field is not that easy because it has to be recalibrated constantly.
Below is represented a R3C2 model, which requires a data commonly unavailable in practice: the wall temperature of the building
Patents registered on this subject can be found on epo.org : EP3291033A1 and EP2781976A1
The R1C1 model is less complicated to implement and still representative of the thermal behavior of a building. To proceed to optimizations, it only requires data easily available with current technologies: indoor and outdoor temperatures, instantaneous heating power.
More information and python codes related to the R1C1 model
The following diagram results from an optimization carried out with the minimize algorithm from the scipy library using the BFGS method.
The blue curve is the field thruth, the green one is the simulation.