Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis

TL;DR

This paper introduces a data-driven multi-fidelity Monte Carlo method using low-fidelity models for efficient uncertainty quantification in plasma turbulence simulations, significantly reducing computational costs.

Contribution

It develops a novel multi-fidelity Monte Carlo approach with sensitivity-driven sparse grid low-fidelity models tailored for plasma turbulence analysis.

Findings

Achieves up to four orders of magnitude efficiency improvement.

Reduces simulation runtime from eight days to one hour.

Effectively handles up to 14 uncertain parameters.

Abstract

The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the background plasma and the magnetic equilibrium. Therefore, uncertainty quantification is essential for achieving predictive numerical simulations of plasma turbulence. However, the high computational costs of the required gyrokinetic simulations and the large number of parameters render standard Monte Carlo techniques intractable. To address this problem, we propose a multi-fidelity Monte Carlo approach in which we employ data-driven low-fidelity models that exploit the structure of the underlying problem such as low intrinsic dimension and anisotropic coupling of the stochastic inputs. The low-fidelity models are efficiently constructed via sensitivity-driven dimension-adaptive sparse grid interpolation using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the power of this method by applying it to two plasma turbulence problems with up to $14$ stochastic parameters, demonstrating that it is up to four orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance, which translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.