  Feature extraction and a neural network model are applied to predict the
defect types and concentrations in experimental TiO$_2$ samples. A dataset of
TiO$_2$ structures with vacancies and interstitials of oxygen and titanium is
built and the structures are relaxed using energy minimization. The features of
the calculated pair distribution functions (PDFs) of these defected structures
are extracted using linear methods (principal component analysis, non-negative
matrix factorization) and non-linear methods (autoencoder, convolutional neural
network). The extracted features are used as the inputs to a neural network
that maps the feature weights to the concentration of each defect type. The
performance of this machine learning pipeline is validated by predicting the
defect concentrations based on experimentally-measured TiO$_2$ PDFs and
comparing the results to brute-force predictions. A physics-based
initialization of the autoencoder has the highest accuracy in predicting the
defect concentrations. This model incorporates physical interpretability and
predictability of material properties, enabling a more efficient material
characterization process with scattering data.
