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High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to…

Machine Learning · Computer Science 2023-01-05 Shaowu Pan , Steven L. Brunton , J. Nathan Kutz

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…

Machine Learning · Statistics 2020-06-19 Aaron Lou , Derek Lim , Isay Katsman , Leo Huang , Qingxuan Jiang , Ser-Nam Lim , Christopher De Sa

Learning radiance fields (NeRF) with powerful 2D diffusion models has garnered popularity for text-to-3D generation. Nevertheless, the implicit 3D representations of NeRF lack explicit modeling of meshes and textures over surfaces, and such…

Computer Vision and Pattern Recognition · Computer Science 2024-09-12 Haibo Yang , Yang Chen , Yingwei Pan , Ting Yao , Zhineng Chen , Zuxuan Wu , Yu-Gang Jiang , Tao Mei

With the introduction of Neural Radiance Fields (NeRFs), novel view synthesis has recently made a big leap forward. At the core, NeRF proposes that each 3D point can emit radiance, allowing to conduct view synthesis using differentiable…

Computer Vision and Pattern Recognition · Computer Science 2023-03-17 Marie-Julie Rakotosaona , Fabian Manhardt , Diego Martin Arroyo , Michael Niemeyer , Abhijit Kundu , Federico Tombari

We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…

Computer Vision and Pattern Recognition · Computer Science 2021-06-25 Chiyu "Max" Jiang , Jingwei Huang , Andrea Tagliasacchi , Leonidas Guibas

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…

Machine Learning · Computer Science 2026-04-07 Zhe Feng , Shilong Tao , Haonan Sun , Shaohan Chen , Zhanxing Zhu , Yunhuai Liu

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…

Machine Learning · Computer Science 2025-11-05 Zhiwen Li , Cheuk Hin Ho , Lok Ming Lui

We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifolds. The existing approaches to learning a distribution on arbitrary manifolds are expensive at inference time, since sampling requires solving a…

Machine Learning · Computer Science 2024-11-26 Peter Sorrenson , Felix Draxler , Armand Rousselot , Sander Hummerich , Ullrich Köthe

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…

Computer Vision and Pattern Recognition · Computer Science 2022-10-11 Chengan He , Jun Saito , James Zachary , Holly Rushmeier , Yi Zhou

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Machine Learning · Computer Science 2025-10-30 Di Zhang

Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we…

Graphics · Computer Science 2024-07-03 Jiaming Peng , Xinhai Chen , Jie Liu

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no…

Computer Vision and Pattern Recognition · Computer Science 2026-05-14 Zhangquan Chen , Puhua Jiang , Mingze Sun , Ruqi Huang

Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D…

Computer Vision and Pattern Recognition · Computer Science 2023-06-06 Xianghui Yang , Guosheng Lin , Zhenghao Chen , Luping Zhou

Very recently neural implicit rendering techniques have been rapidly evolved and shown great advantages in novel view synthesis and 3D scene reconstruction. However, existing neural rendering methods for editing purposes offer limited…

Computer Vision and Pattern Recognition · Computer Science 2022-07-26 Bangbang Yang , Chong Bao , Junyi Zeng , Hujun Bao , Yinda Zhang , Zhaopeng Cui , Guofeng Zhang

We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are…

Graphics · Computer Science 2023-04-18 Zhen Liu , Yao Feng , Michael J. Black , Derek Nowrouzezahrai , Liam Paull , Weiyang Liu

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures.…

Computer Vision and Pattern Recognition · Computer Science 2025-11-18 Lorenzo Olearo , Giulio Viganò , Daniele Baieri , Filippo Maggioli , Simone Melzi

We study the problem of reconstructing 3D feature curves of an object from a set of calibrated multi-view images. To do so, we learn a neural implicit field representing the density distribution of 3D edges which we refer to as Neural Edge…

Computer Vision and Pattern Recognition · Computer Science 2023-03-17 Yunfan Ye , Renjiao Yi , Zhirui Gao , Chenyang Zhu , Zhiping Cai , Kai Xu

We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud,…

Computer Vision and Pattern Recognition · Computer Science 2018-08-06 Nanyang Wang , Yinda Zhang , Zhuwen Li , Yanwei Fu , Wei Liu , Yu-Gang Jiang

Precise representations of 3D faces are beneficial to various computer vision and graphics applications. Due to the data discretization and model linearity, however, it remains challenging to capture accurate identity and expression clues…

Computer Vision and Pattern Recognition · Computer Science 2022-04-26 Mingwu Zheng , Hongyu Yang , Di Huang , Liming Chen

We introduce PolyDiff, the first diffusion-based approach capable of directly generating realistic and diverse 3D polygonal meshes. In contrast to methods that use alternate 3D shape representations (e.g. implicit representations), our…

Computer Vision and Pattern Recognition · Computer Science 2023-12-19 Antonio Alliegro , Yawar Siddiqui , Tatiana Tommasi , Matthias Nießner