Invertible Neural Networks versus MCMC for Posterior Reconstruction in Grazing Incidence X-Ray Fluorescence

TL;DR

This paper introduces an invertible neural network approach for reconstructing posterior distributions in grazing incidence X-ray fluorescence, offering a more efficient alternative to traditional MCMC methods for analyzing nanostructures.

Contribution

The paper presents a novel invertible neural network method for posterior reconstruction that competes with MCMC, providing increased efficiency and flexibility.

Findings

Comparable accuracy to MCMC in posterior reconstruction

Greater computational efficiency

Enhanced flexibility in application scenarios

Abstract

Grazing incidence X-ray fluorescence is a non-destructive technique for analyzing the geometry and compositional parameters of nanostructures appearing e.g. in computer chips. In this paper, we propose to reconstruct the posterior parameter distribution given a noisy measurement generated by the forward model by an appropriately learned invertible neural network. This network resembles the transport map from a reference distribution to the posterior. We demonstrate by numerical comparisons that our method can compete with established Markov Chain Monte Carlo approaches, while being more efficient and flexible in applications.