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

arXiv: https://arxiv.org/abs/2102.03189 · HTML: https://mlsanity.com/paper/2102.03189/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference](https://mlsanity.com/paper/1905.10687/) (2019)
- [Stabilizing Invertible Neural Networks Using Mixture Models](https://mlsanity.com/paper/2009.02994/) (2020)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization](https://mlsanity.com/paper/2004.07871/) (2020)

## Built on by (most cited first, 12 of 12)

- [Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint](https://mlsanity.com/paper/2109.11375/) (2021)
- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2402.04613/) (2024)
- [Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems](https://mlsanity.com/paper/2303.15845/) (2023)
- [WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution](https://mlsanity.com/paper/2201.08157/) (2022)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [Importance Corrected Neural JKO Sampling](https://mlsanity.com/paper/2407.20444/) (2024)
- [Accelerated Stein Variational Gradient Flow](https://mlsanity.com/paper/2503.23462/) (2025)
- [Towards understanding Accelerated Stein Variational Gradient Flow -- Analysis of Generalized Bilinear Kernels for Gaussian target distributions](https://mlsanity.com/paper/2509.04008/) (2025)
- [Mixed Noise and Posterior Estimation with Conditional DeepGEM](https://mlsanity.com/paper/2402.02964/) (2024)
- [Posterior Estimation Using Deep Learning: A Simulation Study of Compartmental Modeling in Dynamic PET](https://mlsanity.com/paper/2303.10057/) (2023)

## Abstract (arXiv)

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.