This thesis investigates the development and application of machine learning (ML) potentials that incorporate long-range interactions, with the goal of enhancing molecular simulations. Traditional ML models, such as neural networks, have been widely used for short-range interactions, effectively modeling local atomic environments. However, they often fail to capture critical long-range interactions that are essential in accurately describing the behavior of large molecular systems. In this work, a new extension of an existing ML approach is presented, leveraging the Fast Multipole Method (FMM) to efficiently approximate long-range interactions within neural network frameworks. This reduces the computational complexity typically associated with direct pairwise calculations.
The proposed model integrates a grid structure, which allows distant atoms to be represented by their collective centers of mass, significantly improving scalability while maintaining accuracy. The method is benchmarked against conventional neural networks and demonstrates improved performance in predicting molecular energies. Results show that this method yields a slighty lower Mean Absolute Error (MAE) compared to models that ignore such interactions. Additionally, suggestions for future improvements are made to further enhance model performance.