A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Approximates smooth surfaces using Laguerre geometry meshes.
Approximates surfaces using Laguerre geometry with spherical faces.
We study the problem of approximating a surface in by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval . As the mesh size $…
AQFC method estimates mesh curvatures using quadratic surfaces.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
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…
Paper generalizes discrete uniformization for genus-zero surfaces.
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, …
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
Random feature model approximates PDE solutions efficiently.
In this work, we explore the idea that effective generative models for point clouds under the autoencoding framework must acknowledge the relationship between a continuous surface, a discretized mesh, and a set of points sampled from the surface. This view motivates a generative model that works by progressively deform…
A new method for nonparametric regression using mesh-based solutions.
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…
Differentiable voxelization for 3D meshes with GPU acceleration.
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…
We create a smooth manifold of triangular meshes with a geodesically complete metric.
Generalized meshes for non-regular geometries, including fractures.
New method improves human mesh recovery for obese people.
Extends geometric decompositions to arbitrary meshes and forms.
The paper explores the topology of polygonal meshes and their properties.
Proposes a new CNN for meshes that can handle orientation.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neur…
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.
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. …
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…
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…
Discrete approximation solves Björling's minimal surface problem.
New method for mesh denoising using TGV of normal vector field.
New method avoids surface self-collision in geometric optimization.
New mesh network preserves symmetries in deep learning.
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability of the corresponding optimal problems in the sense that its complexity is bounded …
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
Unified framework designs LK structures using integer twists on non-manifold meshes.
Optimizes maps with controlled distortion for geometric tasks.
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be -orthogonally decomposed into a curl-free, divergence-free, and a harmonic field. The harmonic field itself can be further decomposed into three component…
Develops weak PINNs for efficient manifold solutions of hyperbolic equations.
Unsupervised mesh disentanglement separates identity and pose.
To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow …
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
Discretizations of the mean curvature and extrinsic curvature components are constructed on piecewise flat simplicial manifolds, giving approximations for smooth curvature values in a mostly mesh-independent way. These constructions are given in combinatoric form in terms of the extrinsic hinge angles, the intrinsic st…
Proposes polynomial neural networks for improved function approximation in various tasks.
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…