# Sensitivity analysis based dimension reduction of multiscale models

## TL;DR

This paper presents a method using sensitivity analysis of single-scale models to reduce input dimensions in multiscale models, thereby enhancing the efficiency of uncertainty quantification, with examples and a counterexample illustrating the approach.

## Contribution

It introduces a sensitivity-based dimension reduction technique for multiscale models and discusses conditions for its valid application.

## Key findings

- Sensitivity analysis can effectively reduce multiscale model input dimensions.
- Excluding uncertain inputs without sensitivity analysis may lead to inaccurate uncertainty estimates.
- The approach is demonstrated with reaction and Ornstein-Uhlenbeck models.

## Abstract

In this paper, the sensitivity analysis of a single scale model is employed in order to reduce the input dimensionality of the related multiscale model, in this way, improving the efficiency of its uncertainty estimation. The approach is illustrated with two examples: a reaction model and the standard Ornstein-Uhlenbeck process. Additionally, a counterexample shows that an uncertain input should not be excluded from uncertainty quantification without estimating the response sensitivity to this parameter. In particular, an analysis of the function defining the relation between single scale components is required to understand whether single scale sensitivity analysis can be used to reduce the dimensionality of the overall multiscale model input space.