{"ID":2847770,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01911","arxiv_id":"2511.01911","title":"Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems","abstract":"Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational principles with quasi-conformal theory. Our approach ensures accurate, bijective mappings by regulating conformality distortion and volume distortion, enabling robust control over deformation quality. The framework is inherently compatible with gradient-based optimization and neural network architectures, making it highly flexible and scalable to higher-dimensional settings. Numerical experiments on both synthetic and real-world medical image data validate the accuracy, robustness, and effectiveness of the proposed method in complex registration scenarios.","short_abstract":"Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational principles with quasi-conformal theory. Our approach ensures accurate, bijective mappi...","url_abs":"https://arxiv.org/abs/2511.01911","url_pdf":"https://arxiv.org/pdf/2511.01911v1","authors":"[\"Zhiwen Li\",\"Cheuk Hin Ho\",\"Lok Ming Lui\"]","published":"2025-10-31T20:39:08Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"math.DG\",\"math.NA\"]","methods":"[]","has_code":false}