S. Schöps

D. Loukrezis, U. Römer, T. Casper et al.

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.

Idoia Cortes Garcia, P. Förster, W. Schilders et al.

Stiff ordinary differential equations (ODEs) play an important role in many scientific and engineering applications. Often, the dependence of the solution of the ODE on additional parameters is of interest, e.g.\ when dealing with uncertainty quantification or design optimization. Directly studying this dependence can quickly become too computationally expensive, such that cheaper surrogate models approximating the solution are of interest. One popular class of surrogate models are Gaussian processes (GPs). They perform well when approximating stationary functions, functions which have a similar level of variation along any given parameter direction, however solutions to stiff ODEs are often characterized by a mixture of regions of rapid and slow variation along the time axis and when dealing with such nonstationary functions, GP performance frequently degrades drastically. We therefore aim to reparameterize stiff ODE solutions based on the available data, to make them appear more stationary and hence recover good GP performance. This approach comes with minimal computational overhead and requires no internal changes to the GP implementation, as it can be seen as a separate preprocessing step. We illustrate the achieved benefits using multiple examples.