A learning method of nonlinear mappings by neural networks with considering their derivatives

This paper discusses a learning method of neural networks for realizing nonlinear mappings with their smoothness on the networks. We proposed an efficient learning method such that neural networks represent not only input-output relations of nonlinear mappings but also their derivatives for arbitrary connected neural networks. The proposed method makes it possible to train a neural network such that the network approximates a nonlinear mapping and its derivative more accurately.