Determining the structural characteristics of impurity-doped quantum dots from spectroscopic measurements represents a challenging inverse problem in semiconductor nanostructure research. In this work, we investigate the feasibility of combining theoretical spectroscopy with machine learning techniques for inverse identification and automated characterization of semiconductor quantum nanostructures. First, the direct problem is solved for a strongly oblate ellipsoidal quantum dot containing multiple hydrogen-like donor impurities using the finite element method. Several impurity arrangements, including linear, central, circular, asymmetric, sinusoidal, and crosswise configurations, are considered for different numbers of impurities and quantum dot sizes. For each configuration, the electron probability density, energy spectrum, and corresponding photoionization cross-section spectra are calculated, forming a synthetic dataset for the inverse analysis. The resulting spectra are then used to train and evaluate two machine learning classifiers: Support Vector Machine (SVM) and a Multi-Layer Perceptron (MLP). The SVM model demonstrates the best performance, achieving a classification accuracy of approximately 94%, while the MLP reaches about 90%. These results indicate that impurity-induced modifications of the photoionization spectra provide distinct spectral fingerprints that enable reliable identification of impurity configurations.