For a few decades, first-principle process models have been used in process systems engineering to design, monitor, and regulate these complicated processes and improve the understanding of the system dynamics. In recent years, dynamic process models have grown even more important in the context of Industry 4.0 and the use of digital twins. The quality and usefulness of digital process models, on the other hand, are highly dependent on the model forecasts' accuracy. The model parameters of the implemented kinetics are crucial and a correct model structure/hypothesis, too. The accuracy of parameter estimates, in turn, is determined by the quantity and quality of the data and the parameter identification solving methodologies used. Here, the standard is still based on the ordinary least squares framework. Alternatively, we present an advanced parameter identification concept that combines systems theory and deep learning ideas. In particular, the parameter identification algorithm is designed as a total least squares optimization problem that incorporates neural ordinary differential equations for surrogate modeling and differential flatness theory for soft-sensor data augmentation. With this augmentation technique, we introduce additional constraints limiting the feasible parameter space. The suggested method's relevance for more accurate and consistent kinetic models is demonstrated in a simulation study of a convection-diffusion problem given in the form of partial differential equations (PDEs). The proposed concept leads to a shift in the parameter sensitivities, and thus, in the accuracy of parameter estimates.