Mean-field theory of power demand prediction in small-sized system via information on timetable and environmental data

We construct a technique of time-series prediction for power consumption in small-sized systems via the mean-field theory (MFT) which approximates Bayesian inference using the expected a posterior (EAP) estimation. Here, we estimate the power consumption as an expectation of an Ising spin averaged over the Boltzmann factor of the Ising model under random fields. Here, we forecast time evolution of power consumption using multiple time-series of power consumptions similar to the target data due to the correlation coefficients, timetable and environmental data, such as the temperature at the target system. Then, we estimate performance of the MFT for a typical small-sized system. Here, we find that controlling fluctuations around the MAP solution is essential for accurate prediction tuning the parameter corresponding to the absolute temperature in statistical physics, and also that accuracy is improved by tuning parameters which correspond to coupling constant between Ising spins and random fields. Then, we find that the accuracy is further improved by tuning random fields which control effects of the timetable and temperatures at the target system.