In this invention, information-fusion and inverse modeling techniques are used to provide real-time, full-field forecast in these devices and system by combining all available information sources, including (1) in-situ monitoring data from sensors, (2) prediction from off-the-shelf numerical models, and (3) empirical knowledge from analysts and engineers. This invention is novel in proposing such a system to be implemented and used in energy-producing devices where sparse data are available from in-situ sensors. If applicable, operation of the device can be adjusted accordingly based on the assimilated results, effectively forming a feedback control loop. The system devised in this invention helps ensure safe and efficient operation of the energy-producing devices such as gas turbines, wind turbine farms. They can also help prevent overheating in data centers and high performance computing server rooms.