Regularity

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Period ending 2026-09-14

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Period ending 2026-09-07

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49 papers

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Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows
Sep 14, 2026Jose Luis Lima de Jesus SilvaRegularity
ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis
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Rethinking Handwritten Character Recognition
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Optimal estimation for Functional Linear Regression with Noisy Discretized Data
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Spectral Convergence of Random Feature Method in Multiple Dimensions
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Grassmann--Plücker Parametrization of Convolutional Filter Subspaces: Regularity and Closed Embeddings
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On Global Regulatability of Robot Manipulators by Classical PID
Sep 1, 2026Cheng Zhao, Jingru Zhu, Lei GuoRobust Control Robotic Manipulator
Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions
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The Axiomatic Trader: Latent Regularity, Information Budgets, and the Canonical Form of a Quantitative Investment System
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Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
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Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations
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Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
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Regularity as seen by Alice and Bob
Jul 15, 2026Omid Yaghoubi, Mikołaj Bojańczyk, Aliaume Lopez +1Computable Regularity
What is a Musical Scale? Regularity and Convention in the Organization of Pitch
Jul 14, 2026John M McBrideMusical Structure Theoretical Foundations
Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width
Jul 12, 2026Yanming Lai, Defeng Sun, Yang WangRectified Linear Unit Networks Regularity
Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity
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Near-Optimal Learning of Gaussian Sobolev Operators
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Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
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Boundary-layer asymptotics for Gaussian-smoothed singular measures
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Tightening the Score Matching Gap for Diffusion Models
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On the stability of scale-space metrics
Jun 25, 2026William LeebWasserstein Distance Regularity
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Probabilistic Operator Learning Regularity
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
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Deep Q-Learning on Hölder Spaces
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Brownian Kernel Ladders
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Range Penalization: Theoretical Insights with Applications in Federated Learning
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Compositional Approximation Can Strictly Outperform Superpositional Approximation
Jun 7, 2026Dennis Elbrächter, Philipp PetersenNeural-Network Approximation Approximation Algorithms
UR-JEPA: Uniform Rectifiability as a Regularizer for Joint-Embedding Predictive Architectures
May 31, 2026Triet M. LeJoint-Embedding Predictive Architectures Sphere-Jepa
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks
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Building Generalization Into Behavior Generation Via Adaptive Compositions of Regularities
May 29, 2026Aravind Battaje, Malte Bernhard, Vito Mengers +1Differentiable Relaxation Regularity
Random Neural Network Expressivity for Non-Linear Partial Differential Equations
May 24, 2026Muhammed Ali Mehmood, Lukas GononPartial Differential Equations Neural-Network Approximation
Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution
May 22, 2026Hongbo Wang, Huaibo Huang, Pin Wang +3Real-World Image Super-Resolution Generative Priors
Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
May 21, 2026Margalit Glasgow, Joan BrunaTwo-Layer Neural Networks Finite Time Analysis
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May 20, 2026Likun Lin, Zhongjian Wang, Jack Xin +1Probability Measures Optimal Transport
Posterior Contraction of Lévy Adaptive B-spline Regression in Besov Spaces
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Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process
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A proximal gradient algorithm for composite log-concave sampling
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Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces
May 12, 2026Jeunghun Oh, Kyeongwon Lee, Jaeyong Lee +1Kolmogorov-Arnold Networks Regularity
Exact ReLU realization of tensor-product refinement iterates
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Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
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Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
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Mean Testing under Truncation beyond Gaussian
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Trajectory-Restricted Optimization Conditions and Geometry-Aware Linear Convergence
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Regularity and Stability Properties of Selective SSMs with Discontinuous Gating
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Structured Approximations of Measures
Oct 13, 2023Keaton Hamm, Varun KhuranaProbability Measures Wasserstein Distance

Sep 14, 2026 · physics.flu-dynJ/K move · Enter open · S save

Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows

Jose Luis Lima de Jesus Silva

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the evolution until viscous decay guarantees regularity for all subsequent times. Applications to cyclic-shear, Arnold-Beltrami-Childress and three-component Taylor-Green fields yield explicit perturbation radii and include initial conditions outside the direct Fourier-Wiener smallness criterion. A parameter-uniform extension covers a connected family of non-Beltrami Taylor-Green centres without repeating the proof for individual parameter values. An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry. Matched neural-operator experiments show that physics-informed training improves physical prediction, while also revealing that these gains do not necessarily improve the discovery of proof-limiting initial conditions. Together, these results provide a reusable method for establishing regularity across prescribed flow families and a quantitative setting for evaluating how learned predictions can assist rigorous computation.