A learning method for vector field approximation by neural networks

The problem of vector held approximation emerges in the wide range of fields such as motion control, computer vision and so on. This paper discusses an approximation method for reconstructing an entire continuous vector field from a sparse set of sample data by neural networks. In order to improve approximation accuracy and efficiency, we incorporate the inherent property of vector fields into the learning problem of neural networks and derive a new learning algorithm. It is shown through numerical experiments that the proposed method makes it possible to reconstruct vector fields accurately and efficiently.