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.