# Fast and Reliable Probabilistic Reflectometry Inversion with Prior-Amortized Neural Posterior Estimation

arXiv: https://arxiv.org/abs/2407.18648 · HTML: https://mlsanity.com/paper/2407.18648/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 26 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Real-time gravitational-wave inference for binary neutron stars using machine learning](https://mlsanity.com/paper/2407.09602/) (2024)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [Effective Sample Size, Dimensionality, and Generalization in Covariate Shift Adaptation](https://mlsanity.com/paper/2010.01184/) (2020)
- [Closing the loop: Autonomous experiments enabled by machine-learning-based online data analysis in synchrotron beamline environments](https://mlsanity.com/paper/2306.11899/) (2023)

## Built on by (most cited first, 4 of 4)

- [Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptation](https://mlsanity.com/paper/2502.02463/) (2025)
- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)
- [Towards real-time surrogate-free Bayesian inversion for neutron reflectometry](https://mlsanity.com/paper/2509.06924/) (2025)
- [GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries](https://mlsanity.com/paper/2509.24117/) (2025)

## Abstract (arXiv)

Reconstructing the structure of thin films and multilayers from measurements of scattered X-rays or neutrons is key to progress in physics, chemistry, and biology. However, finding all structures compatible with reflectometry data is computationally prohibitive for standard algorithms, which typically results in unreliable analysis with only a single potential solution identified. We address this lack of reliability with a probabilistic deep learning method that identifies all realistic structures in seconds, setting new standards in reflectometry. Our method, Prior-Amortized Neural Posterior Estimation (PANPE), combines simulation-based inference with novel adaptive priors that inform the inference network about known structural properties and controllable experimental conditions. PANPE networks support key scenarios such as high-throughput sample characterization, real-time monitoring of evolving structures, or the co-refinement of several experimental data sets, and can be adapted to provide fast, reliable, and flexible inference across many other inverse problems.