I am working on high-dimensional eigenvalue problems stemming from the discretization of linear operators related to dynamical systems. For example, data sets of molecular dynamics simulation and fluid dynamics. The Extended Dynamic Mode Decomposition (EDMD) is a data-driven technique used for approximating the Koopman operator, a linear operator which is particularly useful a linear operator is particularly useful for understanding the behavior of nonlinear dynamical systems from observational data. But solving high-dimensional eigenvalue problems is very challenging in terms of storage consumption and computational robustness. So, I am studying EDMD as a Tensor (a multidimensional generalization of matrices) based method. Tensors arise from a multi-linear structure; for example, when constructing a large basis set of from products of lower-dimensional functions. I am using the Tensor Train(TT) format which is one of the promising candidates for approximating high-dimensional tensors by low-rank decompositions. I am planning to build on these ideas to develop novel and efficient algorithms for these challenging problems.