Internal combustion engines are being required to comply with increasingly stringent government exhaust emissions regulations. Compression ignition (CI) piston engines will continue to be used in cost-sensitive fuel applications such as in heavy-duty buses and trucks, power generation, locomotives and off-highway applications, and will find application in hybrid electric vehicles. Close control of combustion in these engines will be essential to achieve ever-increasing efficiency improvements while meeting increasingly stringent emissions standards. The engines of the future will require significantly more complex control than existing map-based control strategies, having many more degrees of freedom than those of today. Neural network (NN)-based engine modelling offers the potential for a multidimensional, adaptive, learning control system that does not require knowledge of the governing equations for engine performance or the combustion kinetics of emissions formation that a conventional map-based engine model requires. The application of a neural network to model the output torque and exhaust emissions from a modern heavy-duty diesel engine (Navistar T444E) is shown to be able to predict the continuous torque and exhaust emissions from a heavy-duty diesel engine for the Federal heavy-duty engine transient test procedure (FTP) cycle and two random cycles to within 5 per cent of their measured values after only 100 min of transient dynamometer training. Applications of such a neural net model include emissions virtual sensing, on-board diagnostics (OBD) and engine control strategy optimization. (A)