LithoSAGE: Spatially Adaptive and Geometrically Equivariant Neural Operators for Computational Lithography
Abstract
Operator learning offers an efficient surrogate for lithography simulation, replacing costly numerical solutions with direct model inference. However, existing learning architectures are not designed to simultaneously provide geometric equivariance and adaptability to layout windows with different physical extents, and thus their generalization capability is limited. To address this problem, we propose LithoSAGE, a spatially adaptive and geometrically equivariant neural operator method trained on lithography data. Within its basic Fourier neural operator architecture, spectral weights are expressed as continuous functions of normalized radial frequency through a learnable sum of Gaussians. This representation preserves the geometric properties of the lithography system and incorporates rotation and translation equivariance, spatial interaction decay, and direct evaluation on different layout windows. Experiments predict aerial images from mask layouts and resist images from aerial images, demonstrating the geometric equivariance and spatial adaptivity of LithoSAGE. Comparisons with other architectures also assess prediction errors and parameter efficiency.
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BibTeX
@misc{jin2026lithosage,
title = {{LithoSAGE: Spatially Adaptive and Geometrically Equivariant Neural Operators for Computational Lithography}},
author = {Ke Jin and Zhenli Xu and Zilin You},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08001},
eprint = {2611.08001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - LithoSAGE: Spatially Adaptive and Geometrically Equivariant Neural Operators for Computational Lithography
AU - Ke Jin
AU - Zhenli Xu
AU - Zilin You
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08001
UR - https://arxiv.org/abs/2611.08001
AB - Operator learning offers an efficient surrogate for lithography simulation, replacing costly numerical solutions with direct model inference. However, existing learning architectures are not designed to simultaneously provide geometric equivariance and adaptability to layout windows with different physical extents, and thus their generalization capability is limited. To address this problem, we propose LithoSAGE, a spatially adaptive and geometrically equivariant neural operator method trained on lithography data. Within its basic Fourier neural operator architecture, spectral weights are expressed as continuous functions of normalized radial frequency through a learnable sum of Gaussians. This representation preserves the geometric properties of the lithography system and incorporates rotation and translation equivariance, spatial interaction decay, and direct evaluation on different layout windows. Experiments predict aerial images from mask layouts and resist images from aerial images, demonstrating the geometric equivariance and spatial adaptivity of LithoSAGE. Comparisons with other architectures also assess prediction errors and parameter efficiency.
ER -