DLRA and Tensor Networks

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Following discussions with @FHoltorf over Slack, I am opening an issue (feature request) here.

The scope of this FR address the following high level problems:

• How would one solve a high dimensional PDE (think d>12), discretized in the spatial domain using your favourite discretization method, in a low rank format ? Examples include Schroedinger's equations, Black Scholes equations, HJB equations and the like.
• How to perform UQ when your parameter space is infinite dimensional (is a function). Examples include shape optimization, scattering problems, etc. (Of course this only makes sense for the brute force sampling way. But in its defence, the alternative of using some Galerkin expansion for your parameter function may be biased to the choice of the chosen bases; so sampling is a nice way to validate the different Galerkin bases choices.)
• ....

Tensor network extensions to DLRA exist in the works of Christian Lubich.

As @FHoltorf pointed out, using ITensor.jl may be a good idea to implement these algorithms.

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FYI, I am working on something else at this point. So I will get to working on this issue, after that project comes to an end. :)