Tensor representation of non-linear models using cross approximations

Author (s): Aguado, J.V., Borzacchiello, D., Kollepara, K.S., Chinesta, F., and Huerta, A.
Journal: Journal of Scientific Computing

Volume: 81, Issue 1
Pages: 22 – 47
Date: 2019

Abstract:
Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.

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Bibtex:

@article {JVA-ABKCH:19,
        Author = {Jos{\'e} V. Aguado and Domenico Borzacchiello and Kiran S. Kollepara 
                  and Francisco Chinesta and Antonio Huerta},
        Title = {Tensor representation of non-linear models using cross approximations},
        Fjournal = {Journal of Scientific Computing},
        Journal = {J. Sci. Comput.},
        Volume = {81},
        Number = {1},
        Pages = {22--47},
        Year = {2019},
        Doi = {10.1007/s10915-019-00917-2},
        }