Machine learning (ML) offers a versatile and powerful solution for accelerating timeconsuming processes characterized by repeating patterns. In chemistry, ML has found applications in modeling potential energy surfaces (PES), predicting molecular structures, identifying and classifying molecules, enhancing molecular dynamics (MD) simulations, predicting kinetics and other properties, and gaining deeper insights into molecular behavior. To date, and to the best of our knowledge, there are few studies utilizing ML for atmospheric molecular clusters. Our recent studies focused on using kernel ridge regression (KRR) models (implemented in QML ) for modeling the cluster binding energies. Despite its simplicity, KRR achieved chemical accuracy (<1 kcal/mol) when modeling the energies of sulfuric acid-water clusters, using only a few hundred structures for training and the rest of the database for testing. However, Knattrup et al. demonstrated that the computational costs and accuracy of KRR for modeling of density functional theory (DFT) binding energies could be substituted by fast but (compared to DFT) less accurate DFT-3c methods with similar results. Moreover, for accurate modeling, the computational costs of the KRR approach (kernel construction and Cholesky decomposition) almost reach those of QC methods. Additionally, enlarging the configurational space by incorporating more non-equilibrium structures and increasing system complexity by introducing more atom/molecule types would require very large training databases to maintain low errors, increasing costs even further. This work investigates whether neural networks can address these challenges. We utilize one of the commonly applied NN architectures, the polarizable atom interaction neural network (PaiNN), implemented in SchNetPack, to model the energies and forces of typical atmospheric molecular clusters. We demonstrate the accuracy and speed of the trained models and discuss their potential applications in future studies, including those involving large and complex training databases.