The tensor product methodology is one of data compression approaches in mathematical modelling, based mainly on linear algebra. Tensor decompositions offer potentially a significant reduction of the computational burdenâ€¦sometimes cracking problems with 10^{100} or more unknowns that seem otherwise unsolvable. However, as many data-driven techniques, tensor methods are only good if the application under consideration allows that. We found positive examples in uncertainty quantification [1,8], stochastic dynamical systems (Fokker-Planck [18,15], and master [2,7,9] equations), quantum modelling (Schroedinger [11,10] and Liouville-von Neumann [14] equations). Surely, the numerical efficiency depends on all components of the scheme. Sometimes we also needed to develop a better preconditioner [20,5]. The tensor product formalism is also applicable to some nonlinear problems [4, 13].

More details below are structured in the following categories