Emissions released from internal combustion engines (ICEs) should be minimised due to environmental harmful effects and engine performance should be maximised owing to economical concerns. In the recent years, it has been indicated that the Miller cycle applications into the ICEs could provide a remarkable abatement in emissions. Combustion temperatures during heat addition to engine cylinder can be held constant by applying Takemura cycle. This study investigates the maximum performance characteristics such as power, power density and thermal efficiency for the combination of the Miller cycle and the Takemura cycle in seven processes depending on engine speed and ratios of compression, equivalence, exhaust temperature, Takemura cycle, cut-off, cycle pressure, and cycle temperature. An artificial neural network (ANN) modelling approach is also investigated as an alternative and simpler method. The results acquired could be utilised by engine modelers in order to determine the performance characteristics.