High Dimensional Uncertainty Quantification for an Electrothermal Field Problem using Stochastic Collocation on Sparse Grids and Tensor Train Decompositions

TLDR: In this paper, stochastic collocation on sparse grids (SGs) and low-rank tensor decomposition methods, with emphasis on the tensor train (TT) decomposition, are used to solve the curse of dimensionality in ICs.

Abstract: The temperature developed in bondwires of integrated circuits (ICs) is a possible source of malfunction, and has to be taken into account during the design phase of an IC. Due to manufacturing tolerances, a bondwire's geometrical characteristics are uncertain parameters, and as such their impact has to be examined with the use of uncertainty quantification (UQ) methods. Sampling methods, like the Monte Carlo (MC), converge slowly, while efficient alternatives scale badly with respect to the number of considered uncertainties. Possible remedies to this, so-called, curse of dimensionality are sought in the application of stochastic collocation (SC) on sparse grids (SGs) and of the recently emerged low-rank tensor decomposition methods, with emphasis on the tensor train (TT) decomposition.