Tensor Neural Network Interpolation for Efficient High-Dimensional Integration and Solving Non-Tensor-Product-Type Partial Differential Equations

A tensor neural network (TNN) based interpolation method is proposed to efficiently approximate high-dimensional functions that do not have a tensor-product structure. The TNN interpolation enables accurate and efficient computation of high-dimensional integrals, which is crucial for solving high-dimensional partial differential equations with non-tensor-product-type coefficients and source terms using TNN-based machine learning methods.