Source reconstruction using a bilevel optimisation method with a smooth weighted distance function

TL;DR

This paper introduces a bilevel optimization approach using a smooth weighted Mahalanobis distance for inverse atmospheric dispersion problems, demonstrating its effectiveness through toy models and real wind tunnel data.

Contribution

It proposes a novel bilevel optimization framework with a smooth distance function and analyzes conditions for local strict convexity, applied to real-world sensor data.

Findings

The smooth distance function improves inverse problem stability.

Toy models illustrate the convexity and ill-posedness aspects.

Application to wind tunnel data validates the method's practical utility.

Abstract

We consider a bilevel optimatisation method for inverse linear atmospheric dispersion problems where both linear and non-linear model parameters are to be determined. We propose that a smooth weighted Mahalanobis distance function is used and derive sufficient conditions for when the follower problem has local strict convexity. A few toy-models are presented where local strict convexity and ill-posedness of the inverse problem are explored, indeed the smooth distance function is compared and contrasted to linear and piecewise linear ones. The bilevel optimisation method is then applied to sensor data collected in wind tunnel experiments of a neutral gas release in urban environments (MODITIC).