惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

S
Schneier on Security
G
GRAHAM CLULEY
T
Threat Research - Cisco Blogs
Spread Privacy
Spread Privacy
Threat Intelligence Blog | Flashpoint
Threat Intelligence Blog | Flashpoint
NISL@THU
NISL@THU
Latest news
Latest news
N
News and Events Feed by Topic
量子位
爱范儿
爱范儿
M
MIT News - Artificial intelligence
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
GbyAI
GbyAI
A
Arctic Wolf
Google Online Security Blog
Google Online Security Blog
W
WeLiveSecurity
S
Security Affairs
Webroot Blog
Webroot Blog
B
Blog
N
Netflix TechBlog - Medium
Hugging Face - Blog
Hugging Face - Blog
I
InfoQ
博客园 - 司徒正美
H
Heimdal Security Blog
罗磊的独立博客
L
LINUX DO - 最新话题
Security Archives - TechRepublic
Security Archives - TechRepublic
博客园_首页
G
Google Developers Blog
Google DeepMind News
Google DeepMind News
Attack and Defense Labs
Attack and Defense Labs
The Hacker News
The Hacker News
Y
Y Combinator Blog
C
CERT Recently Published Vulnerability Notes
C
Cybersecurity and Infrastructure Security Agency CISA
Cyberwarzone
Cyberwarzone
C
Cisco Blogs
V
Vulnerabilities – Threatpost
T
The Exploit Database - CXSecurity.com
博客园 - 聂微东
Microsoft Azure Blog
Microsoft Azure Blog
人人都是产品经理
人人都是产品经理
The Register - Security
The Register - Security
PCI Perspectives
PCI Perspectives
The GitHub Blog
The GitHub Blog
Jina AI
Jina AI
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
O
OpenAI News
S
Security @ Cisco Blogs
Google DeepMind News
Google DeepMind News

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Learning Decision-Sufficient Representations for Linear Optimization Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses Prabhakar function and unified fractional kinetic equation in bicomplex space Computing Gamma(p/q) with Beta function values Flows on Graded Manifolds Optimal embedding dimension in the Nash--Tognoli theorem An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit Sharp Bohr-Type inequalities for certain classes of close-to-convex functions Invariants of real affine varieties based on their complexifications Topological symmetric and braid homologies A Formal Graph-Theoretic Framework for Pitch Class Set Analysis Finite groups with high commuting probability for Sylow subgroups Performance Bounds for Rollout Policies in Stochastic Shortest Path Problems Real 2-blocks in quasi-simple groups Maximal subalgebras of the Lie algebra $W_n(\mathbb{K})$ Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$ Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Concise and elegant proofs of three formulas for complete Bell polynomials On Reed-Muller subcodes, Grassmannian partitions and sum-free functions Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods A Comprehensive Study of Clique Graphs and Clique Regular Graphs Every signed planar graph is $5$-choosable: A short proof and refinements General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees Democratizing Large-Scale Re-Optimization with LLM-Guided Model Patches On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Stochastic Non-Smooth Convex Optimization with Unbounded Gradients Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space The Geometry of Cooperative Game Solutions: Stratified Egalitarian Shapley Values An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition Amortized Energy-Based Bayesian Inference PyCSP3-Scheduling: A Scheduling Extension for PyCSP3 Strategic PAC Learnability via Geometric Definability Proximal-Based Generative Modeling for Bayesian Inverse Problems Every Minimal Counterexample to the Erdős-Gyárfás Conjecture is Predominantly Cubic SPHERICAL KV: Angle-Domain Attention and Rate-Distortion Retention for Efficient Long-Context Inference NOVA: Fundamental Limits of Knowledge Discovery Through AI Model-based Bootstrap of Controlled Markov Chains TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects Omni-scale Learning-based Sequential Decision Framework for Order Fulfillment of Tote-handling Robotic Systems Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Towards an Inferentialist Account of Information Through Proof-theoretic Semantics Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks QUIVER: Cost-Aware Adaptive Preference Querying in Surrogate-Assisted Evolutionary Multi-Objective Optimization Robust and Fast Training via Per-Sample Clipping Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems Information-Theoretic Measures in AI: A Practical Decision Guide Inference of Online Newton Methods with Nesterov's Accelerated Sketching A Unified Fractional Regularization Framework for Sparse Recovery Mathematical Foundations for Peer-to-Peer Lattice Computation Geometric Layer-wise Approximation Rates for Deep Networks RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory ML-based approach to classification and generation of structured light propagation in turbulent media Zeroth-Order Optimization at the Edge of Stability Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes Training-Free Rate-Distortion-Perception Traversal With Diffusion Conformal Policy Control Linear Regression with Unknown Truncation Beyond Gaussian Features ArcMark: Distortion-Free Multi-Byte LLM Watermark via Optimal Transport Feature Learning Dynamics in Infinite-Depth Neural Networks ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms Normalizing Flows on Quotient Manifolds via Boundary Quotients What Can Be Recovered Under Sparse Adversarial Corruption? Assumption-Free Theory for Linear Measurements TelecomTS: A Multi-Modal Observability Dataset for Time Series and Language Analysis Program Evaluation with Remotely Sensed Outcomes Efficient Gradient Estimation for Parameterized Quantum Systems with Lie Algebraic Symmetries
On the treatment of topology changes on 3D polyhedral moving meshes via 4D space-time hole-like elements in direct ALE ADER-DG methods
[Submitted on 22 May 2026] · 2026-05-25 · via math updates on arXiv.org

View PDF HTML (experimental)

Abstract:This work investigates a novel approach for the high order evolution of hyperbolic PDEs using ADER discontinuous Galerkin schemes within a direct Arbitrary-Lagrangian-Eulerian (ALE) framework on 3D moving polyhedral meshes with topology changes. Our direct ALE method is based on the PDE integration over 4D (3D+time) space-time control volumes connecting the elements of two subsequent tessellations, so to simultaneously evolve the solution both in time and between the two different meshes in an effective and high order manner. In this way, we also avoid any complex and expensive projection-reconstruction techniques and any mesh intersection operation typical of indirect ALE schemes. The crucial step consists in the strategy for building space-time control volumes that also connect elements with different shapes and neighborhoods due to a change in topology. In fact, simply linking existing elements by collapsing or expanding their edges would leave a "hole" in the space-time domain. To fill it, we introduce additional degenerate elements that we call hole-like elements. These are 4D objects with zero 3D volume at both the beginning and end of the timestep, but which possess a strictly non-zero 4D space-time volume. Given the uniqueness of this space-time approach in 3D+time and the necessity of characterizing the geometry of such elements, the main objective of this paper is the formal geometrical and numerical description of the method as well as the presentation of new and intuitive visualization strategies. In particular, we provide a detailed characterization of the hole-like elements arising in correspondence to 2-3, 3-2, and 4-4 flips on the underlying Delaunay tetrahedralization. Finally, we numerically show that the method is fully conservative, satisfies the GCL and maintains the correct order of convergence even in the presence of frequent topology changes.

Submission history

From: Elena Gaburro [view email]
[v1] Fri, 22 May 2026 11:10:00 UTC (14,177 KB)