# Modeling Inverse Ellipsometry Problem via Flow Matching with a Large-Scale Dataset

arXiv: https://arxiv.org/abs/2407.17869 · HTML: https://mlsanity.com/paper/2407.17869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Machine Learning-enhanced Efficient Spectroscopic Ellipsometry Modeling](https://mlsanity.com/paper/2201.04933/) (2022)
- [EllipsoNet: Deep-learning-enabled optical ellipsometry for complex thin films](https://mlsanity.com/paper/2210.05630/) (2022)

## Abstract (arXiv)

Inverse ellipsometry, i.e., reconstructing optical constants and film thickness from the measured phase difference Delta and amplitude ratio Psi, is a fundamentally ill-posed problem. Traditional solutions rely on slow, expert-driven iterative fitting, while the development of machine learning approaches has been severely limited by the lack of large-scale, physically consistent datasets. To address this gap, we introduce EllipBench, a comprehensive benchmark comprising over 8 million high-precision samples spanning 98 thin-film materials and 5 substrates. Building upon this benchmark, we conduct a systematic evaluation of a broad spectrum of methods, including traditional machine learning models, deep neural networks, and Physics-Informed Neural Networks, and show that existing paradigms consistently struggle to fully resolve the inverse ellipsometry task. To better capture its inherent ambiguity, we further propose a novel Decoupled Conditional Flow Matching (DCFM) framework. Rather than formulating the problem as deterministic point-to-point regression, DCFM explicitly decouples geometric film thickness and incorporates it as a robust physical condition to guide a continuous vector field for modeling the inverse probability distribution of wavelength-dependent optical constants. Combined with a gradient detachment strategy and physics-based constraints, our joint architecture effectively mitigates intrinsic physical ambiguities and delivers a robust and accurate solution for inverse ellipsometry.