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

TL;DR

This paper addresses high-dimensional uncertainty quantification in electrothermal IC bondwire temperature modeling by combining stochastic collocation on sparse grids with tensor train decompositions to overcome the curse of dimensionality.

Contribution

It introduces a novel approach integrating stochastic collocation and tensor train decompositions for efficient high-dimensional UQ in electrothermal problems.

Findings

Efficient handling of high-dimensional uncertainties in IC bondwire temperature modeling.

Significant reduction in computational cost compared to traditional sampling methods.

Successful application of tensor train decompositions to complex UQ problems.

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.