In this work, both the mechanistic and semi-mechanistic models are used as a basis for an on-line state estimation technique. The known parts of the semi-mechanistic model are based on first principles, and black-box models consisting of neural networks model the remaining unknown parts. A nonlinear reduced state-observer with variable gain is developed to accommodate both mechanistic and semi-mechanistic models. The observer is designed to possess invariant dynamic modes that can be assigned independently to achieve the desired performance. Convergence of the estimating algorithm can be formulated using Lyapunov stability theorems. Application of the designed observer is demonstrated in a simulation study on a free-radical polymerization reactor system.