A Functional Tensor Train Library in RUST for Numerical Integration and Resolution of Partial Differential Equations

Originally, low-rank tensor decomposition algorithms were designed to approximate high-dimensional tensors. Due to its mathematical characteristics, Tensor-Train decomposition, a type of tensor decomposition that does not necessarily suffer from the curse of dimensionality, has garnered much interest during the past decade. In recent years, Function-Train decomposition, a continuous version of Tensor-Train decomposition, was introduced. This decomposition permits the approximation of high-dimensional functions without function sampling and provides an extensible framework for function integration and differentiation. In this paper, we present a new RUST-based library designed to provide functionality for Function-Train decomposition. In addition, the library offers methods for continuous matrix factorizations and continuous multilinear algebra operations, such as addition, multiplication, integration, differentiation, etc.