The field of geometric deep learning and computational methods is rapidly advancing, with a focus on developing innovative techniques for 3D shape analysis, reconstruction, and processing. Recent research has explored the use of neural networks for tasks such as shape matching, surface reconstruction, and geometry processing. Notably, flow-based models and diffusion-based methods have shown great promise in achieving high-quality results. Additionally, there is a growing interest in developing more efficient and accurate methods for computing topological descriptors and analyzing geometric simplicial complexes. Overall, the field is moving towards more sophisticated and powerful techniques for analyzing and processing complex geometric data. Noteworthy papers include: SplineSplat, which proposes a novel method for 3D ray tracing, and NeuralSSD, which introduces a neural solver for signed distance surface reconstruction. These papers demonstrate the potential of geometric deep learning and computational methods to achieve state-of-the-art results in various applications.
Advances in Geometric Deep Learning and Computational Methods
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Flow matching-based generative models for MIMO channel estimation
SplineSplat: 3D Ray Tracing for Higher-Quality Tomography
Intrinsic Dimension Estimation for Radio Galaxy Zoo using Diffusion Models
Softmax as a Lagrangian-Legendrian Seam
A neural optimization framework for free-boundary diffeomorphic mapping problems and its applications
Toward bilipshiz geometric models
Simplicial covering dimension of extremal concept classes
Learning Conjugate Direction Fields for Planar Quadrilateral Mesh Generation
A Logspace Constructive Proof of L=SL
Too Many or Too Few? Sampling Bounds for Topological Descriptors
DataTransfer: Neural Network-based Interpolation across Unstructured Meshes
FUSE: A Flow-based Mapping Between Shapes
NeuralSSD: A Neural Solver for Signed Distance Surface Reconstruction
Neural Networks-Enabled Channel Reconstruction for Fluid Antenna Systems: A Data-Driven Approach
Learning Compact Latent Space for Representing Neural Signed Distance Functions with High-fidelity Geometry Details
A Neural Field-Based Approach for View Computation & Data Exploration in 3D Urban Environments
B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?
TetraSDF: Precise Mesh Extraction with Multi-resolution Tetrahedral Grid