A general framework for quantifying uncertainty at scale

TL;DR

This paper introduces a sensitivity-driven adaptive sparse grid method that efficiently performs uncertainty quantification and sensitivity analysis on complex, high-dimensional models, demonstrated in fusion research with significant computational savings.

Contribution

The paper presents a novel adaptive sparse grid framework that exploits model structure for scalable uncertainty quantification and sensitivity analysis, especially in high-dimensional, computationally expensive scenarios.

Findings

Reduces computational effort by at least two orders of magnitude.

Provides an accurate surrogate model nine orders of magnitude cheaper than the original.

Successfully applied to turbulent transport in a tokamak with eight uncertain parameters.

Abstract

In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can be investigated explicitly. This prevents straightforward approaches to important tasks like uncertainty quantification and sensitivity analysis. This challenge can be overcome via our recently developed sensitivity-driven dimension adaptive sparse grid interpolation strategy. The method exploits, via adaptivity, the structure of the underlying model (such as lower intrinsic dimensionality and anisotropic coupling of the uncertain inputs) to enable efficient and accurate uncertainty quantification and sensitivity analysis at scale. We demonstrate the efficiency of our approach in the context of fusion research, in a realistic, computationally expensive scenario of turbulent transport in a magnetic confinement tokamak device with eight uncertain parameters, reducing the effort by at least two orders of magnitude. In addition, we show that our method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.