SciPost Physics· 2026Q1
Compressing multivariate functions with tree tensor networks
- 2citations
- Q1SCImago
- 2026year
Short summary
Tree tensor networks (TTNs) offer a more efficient compression format for multivariate functions than the commonly used tensor trains (TTs).
AI-generated from the title and abstract; the full text is not read.
Key points
- Tree tensor networks (TTNs) are introduced as a superior compression format for multivariate functions compared to tensor trains (TTs).
- Direct and interpolative construction methods for representing functions as TTNs are provided.
- TTNs offer significantly more efficient compression for a range of multi-dimensional functions.
- A TTN-based solver for multi-dimensional, non-linear Fredholm equations is demonstrated.
AI-generated from the title and abstract; the full text is not read.
Abstract
Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks—often referred to as tensor trains (TT) or matrix product states (MPS)—are increasingly being used as a numerical Ansatz for continuum functions by ``quantizing’’ the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient Ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.
The authors' abstract, as published at the source. SciPost Physics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Computational Mathematics
Computational MathematicsMathematics