  Based on tensor neural network, we propose an interpolation method for high
dimensional non-tensor-product-type functions. This interpolation scheme is
designed by using the tensor neural network based machine learning method. This
means that we use a tensor neural network to approximate high dimensional
functions which has no tensor product structure. In some sense, the
non-tenor-product-type high dimensional function is transformed to the tensor
neural network which has tensor product structure. It is well known that the
tensor product structure can bring the possibility to design highly accurate
and efficient numerical methods for dealing with high dimensional functions. In
this paper, we will concentrate on computing the high dimensional integrations
and solving high dimensional partial differential equations. The corresponding
numerical methods and numerical examples will be provided to validate the
proposed tensor neural network interpolation.
