arXiv subjects

Enya Shen

Publications and source records attributed to Enya Shen.

10 recordsLinked to original sources

arXiv2026

Walking on Heat Stars for Parabolic Heat Equations with Neumann Boundary Conditions

Monte Carlo methods have proven highly effective for elliptic partial differential equations through algorithms such as Walk on Spheres and Walk on Stars, which evaluate solutions at individual points without volumetric meshing or global linear solves. Extending these methods to the transient regime has remained an open challenge: parabolic equations couple space and time through an anisotropic scaling, requiring joint sampling of spatial displacements and backward time steps whose distribution was not previously available in a unified, exact form. We present Walk on Heat Stars, a grid-free Monte Carlo solver that closes this gap by extending the boundary integral framework of Walk on Stars to the parabolic setting. Our method introduces a non-cylindrical boundary integral formulation that accommodates the time-varying domains induced by heat-ball sampling. The heat ball geometry is parameterized by a logarithmic time coordinate and a spatial direction, revealing that the double-layer kernel factorizes into independent Gamma and uniform components. This parameterization enables exact directional importance sampling of the recursive next walk position, the Neumann flux contribution, and the volumetric source term, yielding unbiased Monte Carlo estimators for all three components. We additionally derive a preliminary gradient estimator that expresses spatial derivatives as weighted boundary integrals of the solution, requiring no recursion on the gradient, and adapt a heteroscedastic regression-based denoiser to the space-time domain for variance reduction. We validate our method on analytical solutions across a range of geometries and spatial frequencies, confirm convergence at the expected Monte Carlo rate, and demonstrate practical applicability on heat sink and cooling scenes with mixed or pure Neumann boundary conditions.

cs.GR↗

arXiv2026

Img2CADSeq: Image-to-CAD Generation via Sequence-Based Diffusion

Boundary Representation (BRep) is the standard format for Computer-Aided Design (CAD), yet reconstructing high-quality BReps from single-view images remains challenging due to the complexity of topological constraints and operation sequences. We present Img2CADSeq, a multi-stage pipeline that overcomes these limitations by encoding CAD sequences into a three-level hierarchical codebook. Guided by an importance prioritization, this strategy values profiles over details, compressing long sequences into a stable discrete latent space. To bridge the modality gap, we leverage a coarse-to-fine point cloud intermediate, aligning 2D visual features with 3D CAD sequences via contrastive learning to condition a VQ-Diffusion model. Supported by newly introduced CAD-220K and PrintCAD datasets, our approach ensures robust industrial domain adaptation. Extensive experiments demonstrate that Img2CADSeq significantly outperforms state-of-the-art methods, producing standard STEP files that can be directly used in commercial CAD software.

cs.CV↗

arXiv2026

Monte Carlo PDE Solvers for Nonlinear Radiative Boundary Conditions

Monte Carlo PDE solvers have become increasingly popular for solving heat-related partial differential equations in geometry processing and computer graphics due to their robustness in handling complex geometries. While existing methods can handle Dirichlet, Neumann, and linear Robin boundary conditions, nonlinear boundary conditions arising from thermal radiation remain largely unexplored. In this paper, we introduce a Picard-style fixed-point iteration framework that enables Monte Carlo PDE solvers to handle nonlinear radiative boundary conditions. While strict theoretical convergence is not generally guaranteed, our method remains stable and empirically convergent with a properly chosen relaxation coefficient. Even with imprecise initial boundary estimates, it progressively approaches the correct solution. Compared to standard linearization strategies, the proposed approach achieves significantly higher accuracy. To further address the high variance inherent in Monte Carlo estimators, we propose a heteroscedastic regression-based denoising technique specifically designed for on-boundary solution estimates, filling a gap left by prior variance reduction methods that focus solely on interior points. We validate our approach through extensive evaluations on synthetic benchmarks and demonstrate its effectiveness on practical heat radiation simulations with complex geometries.

cs.GR↗

arXiv2025

Off-Centered WoS-Type Solvers with Statistical Weighting

Stochastic PDE solvers have emerged as a powerful alternative to traditional discretization-based methods for solving partial differential equations (PDEs), especially in geometry processing and graphics. While off-centered estimators enhance sample reuse in WoS-type Monte Carlo solvers, they introduce correlation artifacts and bias when Green's functions are approximated. In this paper, we propose a statistically weighted off-centered WoS-type estimator that leverages local similarity filtering to selectively combine samples across neighboring evaluation points. Our method balances bias and variance through a principled weighting strategy that suppresses unreliable estimators. We demonstrate our approach's effectiveness on various PDEs,including screened Poisson equations and boundary conditions, achieving consistent improvements over existing solvers such as vanilla Walk on Spheres, mean value caching, and boundary value caching. Our method also naturally extends to gradient field estimation and mixed boundary problems.

cs.GR↗

arXiv2025

Fast and Robust Point Containment Queries on Trimmed Surface

Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness and computational efficiency. We propose a fast and numerically stable method for performing containment queries on trimmed surfaces, including those with periodic parameterizations. Our approach introduces a recursive winding number computation scheme that replaces costly curve subdivision with an ellipse-based bound for Bezier segments, enabling linear-time evaluation. For periodic surfaces, we lift trimming curves to the universal covering space, allowing accurate and consistent winding number computation even for non-contractible or discontinuous loops in parameter domain. Experiments show that our method achieves substantial speedups over existing winding-number algorithms while maintaining high robustness in the presence of geometric noise, open boundaries, and periodic topologies. We further demonstrate its effectiveness in processing real B-Rep models and in robust tessellation of trimmed surfaces.

cs.GR↗

arXiv2023

B-rep Boolean Resulting Model Repair by Correcting Intersection Edges Based on Inference Procedure

As the most essential part of CAD modeling operations, boolean operations on B-rep CAD models often suffer from errors. Errors caused by geometric precision or numerical uncertainty are hard to eliminate. They will reduce the reliability of boolean operations and damage the integrity of the resulting models. And it is difficult to repair false boolean resulting models damaged by errors. In practice, we find that the illegal boolean resulting models stem from the false intersection edges caused by errors. Therefore, this paper proposes an automatic method based on set reasoning to repair flawed structures of the boolean resulting models by correcting their topological intersection edges. We provide a local adaptive tolerance estimation method for each intersection edge based on its geometric features as well as its origin. Then, we propose a set of inference mechanisms based on set operations to infer whether a repair is needed based on the tolerance value and how to correct the inaccurate intersection edge. Our inference strategies are strictly proven, ensuring the reliability and robustness of the repair process. The inference process will transform the problem into a geometric equivalent form less susceptible to errors to get a more accurate intersection edge. Since our inference procedure focuses on topological features, our method can repair the flawed boolean resulting models, no matter what source of errors causes the problem.

cs.GR↗

arXiv2023

Graph Exploration with Embedding-Guided Layouts

Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g., preserve visible communities). Existing hybrid methods that bind the two perspectives still suffer from various generation restrictions (e.g., limited input types and required manual adjustments and prior knowledge of graphs) and the imbalance between aesthetic and exploration goals. In this paper, we propose a flexible embedding-based graph exploration pipeline to enjoy the best of both graph topology and node attributes. First, we leverage embedding algorithms for attributed graphs to encode the two perspectives into latent space. Then, we present an embedding-driven graph layout algorithm, GEGraph, which can achieve aesthetic layouts with better community preservation to support an easy interpretation of the graph structure. Next, graph explorations are extended based on the generated graph layout and insights extracted from the embedding vectors. Illustrated with examples, we build a layout-preserving aggregation method with Focus+Context interaction and a related nodes searching approach with multiple proximity strategies. Finally, we conduct quantitative and qualitative evaluations, a user study, and two case studies to validate our approach.

cs.DS↗

arXiv2022

Visual Data Analysis with Task-based Recommendations

General visualization recommendation systems typically make design decisions for the dataset automatically. However, most of them can only prune meaningless visualizations but fail to recommend targeted results. This paper contributes TaskVis, a task-oriented visualization recommendation system that allows users to select their tasks precisely on the interface. We first summarize a task base with 18 classical analytic tasks by a survey both in academia and industry. On this basis, we maintain a rule base, which extends empirical wisdom with our targeted modeling of the analytic tasks. Then, our rule-based approach enumerates all the candidate visualizations through answer set programming. After that, the generated charts can be ranked by four ranking schemes. Furthermore, we introduce a task-based combination recommendation strategy, leveraging a set of visualizations to give a brief view of the dataset collaboratively. Finally, we evaluate TaskVis through a series of use cases and a user study.

cs.HC↗

arXiv2022

Towards Natural Language Interfaces for Data Visualization: A Survey

Utilizing Visualization-oriented Natural Language Interfaces (V-NLI) as a complementary input modality to direct manipulation for visual analytics can provide an engaging user experience. It enables users to focus on their tasks rather than having to worry about how to operate visualization tools on the interface. In the past two decades, leveraging advanced natural language processing technologies, numerous V-NLI systems have been developed in academic research and commercial software, especially in recent years. In this article, we conduct a comprehensive review of the existing V-NLIs. In order to classify each paper, we develop categorical dimensions based on a classic information visualization pipeline with the extension of a V-NLI layer. The following seven stages are used: query interpretation, data transformation, visual mapping, view transformation, human interaction, dialogue management, and presentation. Finally, we also shed light on several promising directions for future work in the V-NLI community.

cs.HC↗

arXiv2018

Flexible Attributed Network Embedding

Network embedding aims to find a way to encode network by learning an embedding vector for each node in the network. The network often has property information which is highly informative with respect to the node's position and role in the network. Most network embedding methods fail to utilize this information during network representation learning. In this paper, we propose a novel framework, FANE, to integrate structure and property information in the network embedding process. In FANE, we design a network to unify heterogeneity of the two information sources, and define a new random walking strategy to leverage property information and make the two information compensate. FANE is conceptually simple and empirically powerful. It improves over the state-of-the-art methods on Cora dataset classification task by over 5%, more than 10% on WebKB dataset classification task. Experiments also show that the results improve more than the state-of-the-art methods as increasing training size. Moreover, qualitative visualization show that our framework is helpful in network property information exploration. In all, we present a new way for efficiently learning state-of-the-art task-independent representations in complex attributed networks. The source code and datasets of this paper can be obtained from https://github.com/GraphWorld/FANE.

cs.SI↗