# Derivative-based global sensitivity analysis for models with high-dimensional inputs and functional outputs

## TL;DR

This paper introduces a scalable derivative-based global sensitivity analysis framework for complex models with high-dimensional inputs and functional outputs, combining advanced mathematical techniques.

## Contribution

It develops a novel computational approach integrating derivative-based GSA, Karhunen--Loève expansions, and adjoint methods for efficient sensitivity analysis.

## Key findings

- Successfully applied to nonlinear ODE cholera model
- Demonstrated on elliptic PDEs in geosciences
- Showed scalability for high-dimensional problems

## Abstract

We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via Karhunen--Lo\`{e}ve expansions, and adjoint-based gradient computation to provide a scalable computational framework for computing the proposed derivative-based GSA measures. We illustrate the strategy for a nonlinear ODE model of cholera epidemics and for elliptic PDEs with application examples from geosciences and biotransport.