arXiv:2606. 05581v1 Announce Type: cross Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes.
Intrinsic methods fill the default toolbox for geometry processing on meshes. Intrinsic operators, in particular the Laplacian, underlie methods that require invariance to isometry and have hence been employed in many algorithms for shape analysis, learning, and editing.
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation.
arXiv:2608. 07549v1 Announce Type: cross Abstract: Triangle meshes provide explicit and accurate surface geometry, yet their irregular topology connectivity makes 3D mesh tokenization a geometric sampling problem: how to sample and organize geometric evidence into compact, structured and learnable tokens.
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv:2607. 01164v1 Announce Type: new Abstract: Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint.
arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2607. 02564v1 Announce Type: cross Abstract: Computational models of the human heart are widely used to study electromechanical and fluid-dynamical cardiac function and to support applications such as in silico clinical trials.
arXiv:2606. 14334v1 Announce Type: new Abstract: High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension.