Vector Field Approximation by Model Inclusive Learning of Neural Networks

Abstract

The problem of vector field approximation arises in the wide range of fields such as motion control, computer vision and so on. This paper proposes a method for reconstructing an entire continuous vector field from a sparse set of sample data by training neural networks. In order to make approximation results possess inherent properties of vector fields and to attain reasonable approximation accuracy with computational efficiency, we include a priori knowledge on inherent properties of vector fields into the learning problem of neural networks, which we call model inclusive learning. An efficient learning algorithm of neural networks is derived. It is shown through numerical experiments that the proposed method makes it possible to reconstruct vector fields accurately and efficiently.