Nonlinear state estimation is a useful approach to the monitoring of industrial (polymerization) processes. This paper investigates how this approach can be followed to the development of a soft sensor of the product quality (melt index). The bottleneck of the successful application of advanced state estimation algorithms is the identification of models that can accurately describe the process. This paper presents a semi-mechanistic modeling approach where neural networks describe the unknown phenomena of the system that cannot be formulated by prior knowledge based differential equations. Since in the presented semimechanistic model structure the neural network is a part of a nonlinear algebraicdifferential equation set, there are no available direct input-output data to train the weights of the network. To handle this problem in this paper a simple, yet practically useful spline-smoothing based technique has been used. The results show that the developed semi-mechanistic model can b...