Some Thoughts on Compositional Tensor Networks

Reinhold Schneider () and Mathias Oster ()
Additional contact information
Reinhold Schneider: TU Berlin, Department of Mathematics
Mathias Oster: RWTH Aachen

A chapter in Multiscale, Nonlinear and Adaptive Approximation II, 2024, pp 419-447 from Springer

Abstract: Abstract In these notes we present some first ideas on the composition of tensor trains for the use in scientific computing. We discuss the relation to deep neural networks and the potential role compositional tensor trains can have in efficiently representing the solutions to PDEs. We illustrate the potential role compositional tensor trains might have for efficiently representing the solutions to high-dimensional PDEs circumventing the curse of dimensionality. Lastly, we embed the task of function regression on the set of compositional tensor trains into the context of semiglobal optimal control and mean field games.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-75802-7_19

Ordering information: This item can be ordered from
http://www.springer.com/9783031758027

DOI: 10.1007/978-3-031-75802-7_19

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().