Due to the curse of dimensionality, the simulation and analysis of high-dimensional problems is often infeasible. One way to mitigate this is to use tensor-based methods. Tensors, in our sense, are just multidimensional arrays and can be seen as generalizations of vectors and matrices. Instead of storing the full tensor, low-rank tensor decompositions are computed (using SVDs or QR decompositions).

In this seminar, we will consider different tensor formats (canonical, tensor train, Tucker) and applications ranging from chemical reaction networks to fluid flow problems.