Future wireless networks depend on the development of new mechanisms that can increase the efficiency of the network. Antenna array adaptive beamforming (ABF) is an antenna operation that can be significantly improved with the use of machine learning. In this paper, a deterministic beamforming technique is compared with two different types of neural networks (NNs). These are the non-linear autoregressive network with exogenous inputs (NARX) and the recurrent NN (RNN) with long short-term memory (LSTM) units. To train the NNs, we produce a dataset using the minimum variance distortionless algorithm (MVDR) applied to a realistic antenna array. Using grid search, we find the best architecture for both NNs. Then, we train the final models and evaluate them by comparing their accuracy to that of the MVDR algorithm. We demonstrate how the use of NNs is preferable to that of deterministic algorithms as they appear to maintain high accuracy while having a much lower response time than that of deterministic algorithms. The RNN with LSTM units is the most promising out of the two NN models as it achieves higher accuracy with a slightly shorter training time.