Calculation of transport coefficient profiles in modulation experiments as an inverse problem

TL;DR

This paper introduces a matricial reformulation for calculating transport profiles in modulation experiments, addressing ill-conditioning issues and improving the accuracy and uncertainty assessment of transport code calculations.

Contribution

A novel matricial approach for inverse problems in transport profile calculation that clarifies accuracy issues and enhances uncertainty quantification.

Findings

Reformulation reveals conditions causing ill-conditioning.

Improved accuracy in transport profile calculations.

Enhanced uncertainty assessment methods.

Abstract

The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusion model where these issues are related to the vanishing of the determinant of a 2x2 matrix. This sheds light on the accuracy of calculations with transport codes, and provides a path for a more precise assessment of the profiles and of the related uncertainty.