Abstract: Methods and apparatuses that generate a simulation object for a physical system are described. The simulation object includes a trained computing structure to determine future output data of the physical system in real time. The computing structure is trained with a plurality of input units and one or more output units. The plurality of input units include regular input units to receive input data and output data of the physical system. The output units include one or more regular output units to predict a dynamic rate of change of the input data over a period of time. The input data and output data of the physical system are obtained for training the computing structure. The input data represent a dynamic input excitation to the physical system over the period of time. And the output data represents a dynamic output response of the physical system to the dynamic input excitation over the period of time.