New approach uses isotropic geometry to solve Euclidean problems.
problem Solving systems of constraints in Euclidean geometry.
method Start with analogous problems in isotropic geometry to initialize optimization algorithms.
result Solutions in isotropic geometry provide insight and initialize Euclidean problem solutions.
Differentiable voxelization for 3D meshes with GPU acceleration.
problem Efficient and accurate voxelization of 3D meshes.
method Differentiable voxelization using winding number and solid angles, with GPU acceleration and neural network deformation.
result State-of-the-art performance in accuracy and efficiency on the ShapeNet dataset.
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…
The worldwide surge of multiresistant microbial strains has propelled the search for alternative treatment options. The study of Protein-Protein Interactions (PPIs) has been a cornerstone in the clarification of complex physiological and pathogenic processes, thus being a priority for the identification of vital compon…
We create a smooth manifold of triangular meshes with a geodesically complete metric.
problem Representing and manipulating 2D shapes as triangular meshes.
method Developed a geodesically complete Riemannian metric for triangular meshes.
result The metric preserves mesh connectivity and avoids mesh degradation.
Generalized meshes for non-regular geometries, including fractures.
problem Discretization of partial differential equations in non-regular geometries.
method Introduces generalized meshes with overlapping elements and flexible adjacency relations.
result Discrete differential forms on virtually inflated meshes characterize the trace space of forms in surrounding volumes.
In this paper, we propose the use of a black-box optimization method called deterministic Mesh Adaptive Direct Search (MADS) algorithm with orthogonal directions (Ortho-MADS) for the selection of hyperparameters of Support Vector Machines with a Gaussian kernel. Different from most of the methods in the literature that…
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
problem Efficiently modeling 3D geometry for computer graphics, robotics, and games.
method Transformer-based autoregressive model for predicting mesh vertices and faces.
result PolyGen produces high-quality, usable 3D meshes and competitive conditional performance.
New method improves human mesh recovery for obese people.
problem Improving mesh recovery for obese people.
method Generative optimization of mesh parameters from 2D keypoints.
result Significant improvement in mesh recovery performance on obese person images.
Extends geometric decompositions to arbitrary meshes and forms.
problem Constructing local bases for finite element spaces on arbitrary meshes.
method Generalizes extension operators to arbitrary meshes and forms, showing they yield geometric decompositions.
result Extension operators yield geometric decompositions for arbitrary meshes and forms.
The paper explores the topology of polygonal meshes and their properties.
problem Understanding the topological properties of polygonal meshes.
method Overview of topological concepts, definitions of intrinsic and extrinsic topology, proofs of Euler and Euler-Poincaré formulas, and discussion on cutting meshes.
result Detailed understanding and definitions of polygonal mesh topology, including intrinsic and extrinsic properties.
Proposes a new CNN for meshes that can handle orientation.
problem Isotropic kernels in graph convolutions are insensitive to mesh geometry.
method Introduces gauge equivariant kernels and geometric message passing.
result Significantly improved expressivity over conventional GCNs.
AQFC method estimates mesh curvatures using quadratic surfaces.
problem Estimating curvatures for irregular polygonal meshes.
method Local approximation of vertices and normals by quadratic surfaces, computed as implicit surfaces.
result AQFC provides robust curvature estimation for irregular meshes.
Approximates smooth surfaces using Laguerre geometry meshes.
problem Approximating smooth surfaces in Laguerre geometry.
method Using Laguerre meshes composed of quadrilaterals, cones, and spherical faces.
result Laguerre conjugate nets and directions for surface approximation.
Two algorithms create high-quality triangular meshes for surfaces with guaranteed angles.
problem Creating high-quality triangular meshes for surfaces with controlled angles.
method MidNormal and GradNormal algorithms generate meshes with specified angle constraints.
result Meshes converge to surfaces as mesh size decreases, maintaining specified angles.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
problem Invalidity of existing inverse theorems for mesh group-planes.
method Classification of three and five point meshes, analysis of joint invariant signatures.
result Valid conditions for the Signature-inverse Theorem in mesh group-planes.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
problem Understanding the spectral properties of mesh matrices of graphs.
method Definition and study of mesh matrices, introduction of mesh Laplacian, derivation of characteristic polynomial formulas.
result Mesh Laplacian eigenvalues are all real and greater than or equal to 1, with a smallest positive eigenvalue estimated.
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volu…
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
Eliciting semantic similarity between concepts in the biomedical domain remains a challenging task. Recent approaches founded on embedding vectors have gained in popularity as they risen to efficiently capture semantic relationships The underlying idea is that two words that have close meaning gather similar contexts. …
A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of inform…
Approximates surfaces using Laguerre geometry with spherical faces.
problem Approximating smooth surfaces using Laguerre geometry.
method Using Laguerre conjugate nets and spherical faces to approximate surfaces.
result Laguerre conjugate nets provide a method for surface approximation.
Generative model creates high-quality meshes from point clouds.
problem Creating accurate meshes from point cloud data.
method Modeling point cloud generation as sphere deformation through deep neural networks.
result The model efficiently generates high-quality meshes from point clouds.
New method for mesh denoising using TGV of normal vector field.
problem Improving mesh quality by removing noise.
method Proposes a novel TGV formulation for normal vector fields on triangular meshes.
result New method outperforms existing techniques in mesh denoising experiments.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
New mesh network preserves symmetries in deep learning.
problem No existing mesh processing architecture is equivariant to all symmetries.
method Equivariant attention-based mesh network using relative tangential features.
result The network achieves improved performance and is equivariant to various transformations.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
problem Computing uniformizations for surfaces of genus >1.
method Discrete conformality and uniformization on triangle meshes.
result Discrete uniformizations approximate continuous uniformization for closed surfaces of genus ≥1.
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
problem Discrete representation of continuous vector-valued environmental data.
method Develops discrete intrinsic Gaussian processes for vector-valued data on triangular meshes using discrete differential operators.
result Models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data.
Unified framework designs LK structures using integer twists on non-manifold meshes.
problem Binary twisting limits topological possibilities and structural behaviors.
method Generalizes twist formulation to arbitrary integer labels for non-manifold meshes.
result Integer twists enable full connectivity and dynamic folding/articulation.
Paper studies superconvergence on surface meshes using gradient recovery.
problem Proving superconvergence on deviated surfaces.
method Introduces geometric supercloseness and an algorithmic framework for gradient recovery.
result Validates theoretical results with numerical examples.
Unsupervised mesh disentanglement separates identity and pose.
problem Geometric disentanglement for 3D deformable models.
method CFAN-VAE architecture using conformal factor and normal features.
result CFAN-VAE achieves state-of-the-art performance on unsupervised geometric disentanglement.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
Paper generalizes discrete uniformization for genus-zero surfaces.
problem Discrete uniformization for surfaces of genus zero.
method Reduction to planar cases via stereographic projections.
result Generalization of discrete uniformization to genus-zero surfaces.
Unified inference framework for spatiotemporal data.
problem Challenges in extracting mechanistic insights from complex spatiotemporal data.
method Vision transformer-driven variational encoding and likelihood-free Bayesian approach.
result Unified inference framework for identifying spatial and temporal patterns.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By exploiting the ordering property of semi-regular meshes, the convolution is defin…
In this short paper we investigate whether meta-learning techniques can be used to more effectively tune the hyperparameters of machine learning models using successive halving (SH). We propose a novel variant of the SH algorithm (MeSH), that uses meta-regressors to determine which candidate configurations should be el…
Physics-guided deep learning improves CFD for bubbly flow simulations.
problem Accurate CFD prediction of two-phase bubbly flow with high computational efficiency.
method Developed a multi-scale framework with Feature Similarity Measurement (FSM) for error estimation and a physics-guided deep feedforward neural network (DFNN) surrogate model.
result Physics-guided deep learning achieves comparable accuracy to fine-mesh simulations with fast-running feature.
A new method for nonparametric regression using mesh-based solutions.
problem Estimating regression functions non-parametrically with computational tractability.
method Mesh-based approximate solution (MBS) for penalized regression problems.
result MBS transforms NPR to a discrete convex minimization problem, making it computationally feasible.
CupNet prunes neural nets for cup-shaped data.
problem Pruning neural networks for cup-shaped data.
method Used simulated cup drawing data to prune a neural network.
result Pruning effectively reduces network size for cup-shaped data.
Generative modeling of 3D shapes has become an important problem due to its relevance to many applications across Computer Vision, Graphics, and VR. In this paper we build upon recently introduced 3D mesh-convolutional Variational AutoEncoders which have shown great promise for learning rich representations of deformab…
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We s…
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
problem Developing a more accurate discrete Laplacian for 3D meshes.
method Proves the Euler-Lagrange equation for the Dirichlet energy using the associated discrete Laplacian of the dual construction.
result The associated discrete Laplacian is optimal in R3 compared to the primal construction. A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.