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Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To highly speed up training, we created a novel shallow 4-layer ANN called "Pairwise Neural Network" ("PairNet") with high-speed hyperparameter optimization. In addition, a value of each input is partitioned into multiple intervals, and then an n-dimensional space is partitioned into M n-dimensional subspaces. M local PairNets are built in M partitioned local n-dimensional subspaces. A local PairNet is trained very quickly with only one epoch since its hyperparameters are directly optimized one-time via simply solving a system of linear equations by using the multivariate least squares fitting method. Simulation results for three regression problems indicated that the PairNet achieved much higher speeds and lower average testing mean squared errors (MSEs) for the three cases, and lower average training MSEs for two cases than the traditional ANNs. A significant future work is to develop better and faster optimization algorithms based on intelligent methods and parallel computing methods to optimize both partitioned subspaces and hyperparameters to build the fast and effective PairNets for applications in big data mining and real-time machine learning.