<title>Abstract</title>
To achieve high thermal efficiency and low emission in automobile engines, advanced combustion technologies using compression auto-ignition of premixtures have been studied, and model-based control has attracted attention for their practical applications. Although simplified physical models have been developed for model-based control, appropriate values for their model parameters vary depending on the operating conditions, engine driving environment, and engine aging. Herein, we studied an onboard adaptation method of model parameters in a heat release rate (HRR) model. This method adapts the model parameters using neural networks considering the operating conditions and can respond to the driving environment and the engine aging by training the neural networks onboard. Detailed studies were conducted regarding the training methods. Compared to when the model parameters were set as constants, this adaptation method significantly improved the prediction accuracy of the HRR model. Furthermore, control tests on an engine bench showed that this adaptation method also improved the model-based control accuracy of the HRR.