On the optimality of dimension truncation error rates for a class of parametric partial differential equations
arXiv:2511.01492
The paper analyzes the error introduced when infinite-dimensional random field inputs in parametric PDEs are truncated to finite dimensions, and proves that the known dimension‑truncation error rates are optimal for two specific model problems.
Abstract
In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of independent and identically distributed random variables. The lognormal random field is a prime example of such a model. While there have been many studies assessing the error in the PDE response that occurs when an infinite-dimensional random field input is replaced with a finite-dimensional random field, there do not seem to be any analyses in the existing literature discussing the sharpness of these bounds. This work seeks to remedy the situation. Specifically, we investigate two model problems where the existing dimension truncation error rates can be shown to be sharp.
8 pages