International workshop on tensor cross interpolation and other algorithms for learning tensor networks

Tensor network techniques are well-established numerical tools for solving seemingly exponentially hard problems in quantum many-body physics, with important successes in the simulation of model correlated electronic systems, quantum magnetisms and quantum computers. In this type of application, tensor networks are used to obtain compressed representations of quantum many-body wave functions, allowing for an exponential speed-up of otherwise impossible calculations.

In the last few years, tensor network methods have spread far beyond applications in many-body physics, due to two key developments. First, it has been realized that many mathematical objects encountered in computational physics, such as the solutions of partial differential equations, are compressible too and admit low-rank tensor network representations. These enable manipulations of functions (integration, convolution, Fourier transform, ...) to be performed exponentiallyfaster. Second, new exponentially fast learning algorithms are emerging for finding accurate tensor network representations of huge but compressible tensors – a key example being tensor cross interpolation (TCI). These algorithms – akin to machine learning – find compact representations of the entire object from a tiny training data set.

Together, these two developments provide a path for transferring much of the tensor network methodology developed for quantum many-body computations to entirely new classes of mathematical problems, such as high-dimensional integrals, partial differential equations, or function optimization. New applications, e.g. in computational fluid dynamics,  plasma physics, optimized basis sets in chemistry, evaluation of Feynman diagrams in quantum field theory, to name but a few, are rapidly emerging.

This workshop will gather important players in this emerging field, from both the applied mathematics and theoretical physics communities, to discuss these exciting new applications and algorithms. This workshop is inspired by activities within the tensor4all collaboration (https://tensor4all.org/). The schedule will be kept relatively light to leave much room for scientific discussions.