An adaptive dynamical low-rank tensor approximation scheme for fast circuit simulation

Abstract

Tensors, as higher order generalization of matrices, have received growing attention due to their readiness in representing multidimensional data intrinsic to numerous engineering problems. This paper develops an efficient and accurate dynamical update algorithm for the low-rank mode factors. By means of tangent space projection onto the low-rank tensor manifold, the repeated computation of a full tensor Tucker decomposition is replaced with a much simpler solution of nonlinear differential equations governing the tensor mode factors. A worked-out numerical example demonstrates the excellent efficiency and scalability of the proposed dynamical approximation scheme.