Diffraction gratings have a wide array of applications in optics, diagnostics, food science, sensing, and process inspection. Scattering effects from defects can severely degrade the performance of such gratings. In this paper, we consider three classes of defects: Two classes introduced at the grating/air interface, as a change in line heights, and one class introduced as a sinusoidal variation of the grating/substrate interface. The scattering properties of the gratings are modelled using rigorous coupled wave analysis, and defects are approximated with a new semi-analytical model and a neural network. The new methods make it possible to avoid the time consuming library generation/search strategy commonly used in scatterometry. The method does not introduce new numerical parameters, and therefore no new parameter correlations. This work enables improved grating reconstruction, especially of non-diffracting short pitch gratings. It is found that two of the defect classes can be adequately described by the semi-analytical model, while the third defect is accurately reconstructed by a neural network. The network is demonstrated to be faster than a library search and more versatile for related structures.