Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space.
arXiv:2606. 13400v1 Announce Type: cross Abstract: While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements.
Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support.
arXiv:2607. 14652v1 Announce Type: new Abstract: Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions.
Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function.
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:2608. 09938v1 Announce Type: cross Abstract: Hyperelastic deformations are highly sensitive to domain geometry and boundary conditions, making generalization across both a critical capability for neural operators applied to these problems.
arXiv:2505. 04486v4 Announce Type: replace-cross Abstract: Flow matching models have shown great potential in image generation tasks among probabilistic generative models.
arXiv:2606. 12994v2 Announce Type: replace Abstract: Data-driven engineering design is constrained by the lack of large-scale 3D datasets that pair geometry with physics-based performance labels.
arXiv:2605. 01171v2 Announce Type: replace-cross Abstract: Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets.
arXiv:2607. 05568v1 Announce Type: cross Abstract: Representing 3D shapes as compact sets of geometric primitives is fundamental to robotics, simulation, and scene understanding.
arXiv:2608. 10544v1 Announce Type: cross Abstract: Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations.
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.