PoissonNet: A Local-Global Approach for Learning on Surfaces

• URL: http://arxiv.org/abs/2510.14146v1
• Date: Wed, 15 Oct 2025 22:25:44 GMT
• Title: PoissonNet: A Local-Global Approach for Learning on Surfaces
• Authors: Arman Maesumi, Tanish Makadia, Thibault Groueix, Vladimir G. Kim, Daniel Ritchie, Noam Aigerman,
• Abstract summary: We introduce PoissonNet, a novel neural architecture for learning on meshes.<n>Our construction is efficient, requiring far less compute overhead than comparable methods.<n>As a central application, we show its ability to learn deformations, significantly outperforming state-of-the-art architectures that learn on surfaces.
• Score: 31.598472309890116
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient computational overhead. Drawing from classic local-global approaches in mesh processing, we introduce PoissonNet, a novel neural architecture that overcomes all of these deficiencies by formulating a local-global learning scheme, which uses Poisson's equation as the primary mechanism for feature propagation. Our core network block is simple; we apply learned local feature transformations in the gradient domain of the mesh, then solve a Poisson system to propagate scalar feature updates across the surface globally. Our local-global learning framework preserves the features's full frequency spectrum and provides a truly global receptive field, while remaining agnostic to mesh triangulation. Our construction is efficient, requiring far less compute overhead than comparable methods, which enables scalability -- both in the size of our datasets, and the size of individual training samples. These qualities are validated on various experiments where, compared to previous intrinsic architectures, we attain state-of-the-art performance on semantic segmentation and parameterizing highly-detailed animated surfaces. Finally, as a central application of PoissonNet, we show its ability to learn deformations, significantly outperforming state-of-the-art architectures that learn on surfaces.

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