# Large Scale Mask Optimization Via Convolutional Fourier Neural Operator and Litho-Guided Self Training

arXiv: https://arxiv.org/abs/2207.04056 · HTML: https://mlsanity.com/paper/2207.04056/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [DAMO: Deep Agile Mask Optimization for Full Chip Scale](https://mlsanity.com/paper/2008.00806/) (2020)
- [Generic Lithography Modeling with Dual-band Optics-Inspired Neural Networks](https://mlsanity.com/paper/2203.08616/) (2022)

## Built on by (most cited first, 8 of 8)

- [ILILT: Implicit Learning of Inverse Lithography Technologies](https://mlsanity.com/paper/2405.03574/) (2024)
- [Fast inverse lithography based on a model-driven block stacking convolutional neural network](https://mlsanity.com/paper/2412.14599/) (2024)
- [MaskOpt: A Large-Scale Mask Optimization Dataset to Advance AI in Integrated Circuit Manufacturing](https://mlsanity.com/paper/2512.20655/) (2025)
- [Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems](https://mlsanity.com/paper/2608.29888/) (2026)
- [Neural Lithography: Close the Design-to-Manufacturing Gap in Computational Optics with a 'Real2Sim' Learned Photolithography Simulator](https://mlsanity.com/paper/2309.17343/) (2023)
- [A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media](https://mlsanity.com/paper/2402.11568/) (2024)
- [MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning](https://mlsanity.com/paper/2605.12528/) (2026)
- [LithoGRPO: Fast Inverse Lithography via GRPO Reinforced Flow Matching](https://mlsanity.com/paper/2606.00228/) (2026)

## Abstract (arXiv)

Machine learning techniques have been extensively studied for mask optimization problems, aiming at better mask printability, shorter turnaround time, better mask manufacturability, and so on. However, most of these researches are focusing on the initial solution generation of small design regions. To further realize the potential of machine learning techniques on mask optimization tasks, we present a Convolutional Fourier Neural Operator (CFNO) that can efficiently learn layout tile dependencies and hence promise stitch-less large-scale mask optimization with the limited intervention of legacy tools. We discover the possibility of litho-guided self-training (LGST) through a trained machine learning model when solving non-convex optimization problems, which allows iterative model and dataset update and brings significant model performance improvement. Experimental results show that, for the first time, our machine learning-based framework outperforms state-of-the-art academic numerical mask optimizers with an order of magnitude speedup.