Sparse Random Feature Expansions for Surrogate Modelling

Surrogate models are indispensable tools for conducting uncertainty quantification and robustness analyses, thereby driving pivotal design decisions, such as those involved in automotive engineering. The necessity for surrogate models arises from the reality that simulations of an object encapsulate inherent uncertainties concerning parameters and model definitions, and these simulations are computationally costly. Consequently, they yield a minimal number of observations in relation to their high-dimensional domain. As a result, the crux of the challenge lies in accurately fitting a function $f_{\theta}$ within a sparse space that can approximate a complex simulation to a sufficient degree, thereby enabling us to derive meaningful conclusions.

In this presentation, I will share key findings from my master’s thesis, focusing primarily on the concept of random feature expansion and its application in surrogate modelling.