Has anybody stumbled upon any kind of application of high-frequency high-dimensional problems ($d\geq 4$)?
My interest comes from the following: there is quite a decent amount of papers where people consider efficient representation of discretized integral operators in $d$ dimensions that allows to avoid a curse of dimensionality (tensor decomposition methods); namely, $d$-dimensional Laplace operator seems to be of an importance for quantum mechanics community. Is there any interest in working with $d$-dimensional Helmholtz equation, for example?
I heard as well that statistical applications require efficient representation of high-dimensional functions, but still, I have never seen anybody dealing with low-rank representations of multidimensional oscillatory functions unless it was a question of mainly theoretical interest.
Thank you in advance