- Introduction
In the last two decade, tensor computations developed from a small and little known subject to a vast and heterogeneous field with many diverse topics ranging from high-order decomposition and low-rank approximation to optimization and multi-linear contractions. At the same time, several of these operations with tensors are progressively and diversely applied to many, rather distinct domains; from Quantum Chemistry to Deep Learning, and from Condensed Matter Physics to Remote Sensing. These domain-specific applications of tensor computations present a number of particular challenges originating from their high dimensionality, computational cost, and complexity. Usually, because these challenges could be quite diverse among application areas, there is not an homogeneous and uniform approach in the development of software programs tackling tensor operations. On the contrary, very often developers implement domain-specific libraries which compromise their use acrossIntroduction
In the last two decade, tensor computations developed from a small and little known subject to a vast and heterogeneous field with many diverse topics ranging from high-order decomposition and low-rank approximation to optimization and multi-linear contractions. At the same time, several of these operations with tensors are progressively and diversely applied to many, rather distinct domains; from Quantum Chemistry to Deep Learning, and from Condensed Matter Physics to Remote Sensing. These domain-specific applications of tensor computations present a number of particular challenges originating from their high dimensionality, computational cost, and complexity. Usually, because these challenges could be quite diverse among application areas, there is not an homogeneous and uniform approach in the development of software programs tackling tensor operations. On the contrary, very often developers implement domain-specific libraries which compromise their use across disciplines. The end result is a fragmented community where efforts are often replicated and scattered [1].
This Research Topic represents an attempt in bringing together different communities, spearheading the latest cutting-edge results at the frontier of tensor computations, and sharing the lessons learned in domain-specific applications. The issue includes ten research articles written by experts in the field. For the sake of clarity, the articles can be somewhat artificially divided in four main areas: (i) decompositions, (ii) low-rank approximations, (iii) high-performance operations, and (iv) tensor networks. In practice, many of the works in this Research Topic spill over the boundaries of such areas and are interdisciplinary in nature, thus demonstrating how cross-fertilizing the field of tensor computations is.…
