Neural-Network Approximation

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Period ending 2026-09-07

3 new papers

A weekly snapshot of new work published in Neural-Network Approximation.

102 papers

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  1. Learning Lyapunov Operators for Nonlinear Systems

    Sep 16, 2026Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1Fourier Neural OperatorsNeural-Network Approximation

  2. Physics Informed Random Feature Neural Networks for Solving PDEs

    Sep 14, 2026Chi-An Chen, Chunyang Liao, Ming ZhongNeural-Network Approximation

  3. ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis

    Sep 14, 2026Shuhao JiaoNeural-Network ApproximationRegularity

  4. Draining Fictitious Knots: Restoring Distance-Awareness Guarantees for High-Dimensional Spline Networks

    Sep 14, 2026Masoud Ataei, Mohammad Javad Khojasteh, Vikas DhimanKolmogorov-Arnold NetworksB-Spline

  5. Residual neural networks overcome the curse of dimensionality for semilinear heat equations

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaNeural-Network ApproximationResidual Connections

  6. Sharp Approximation Rates for Neural Networks with Affine Latent Parameterizations

    Aug 31, 2026Shijun ZhangNeural-Network ApproximationArtificial Neural Networks

  7. Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization

    Aug 31, 2026Jessica D. Elrefaei, Kaixun Hua, Seungbae Kim +2Bilevel OptimizationMixed-Integer Linear Programming

  8. Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

    Aug 10, 2026Konrad Kleinberg, Thomas KruseNeural-Network ApproximationStochastic Differential Equations

  9. Approximation Rates for Metaplectic Neural Networks

    Aug 9, 2026Ahmed Abdeljawad, Marcello Carioni, Elena CorderoNeural-Network ApproximationTwo-Layer Neural Networks

  10. A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise

    Aug 8, 2026Nacira Agram, Reda Hmioui, Jan RemsNeural-Network ApproximationFokker--Planck Equation

  11. Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

    Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural-Network ApproximationSolution Operator

  12. Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

    Aug 5, 2026Khemraj Shukla, George Em KarniadakisFourier Neural OperatorsNeural Operators

  13. Universal Function Approximation via Diffractive Optical Processors: Physical Limits, Error Bounds, and Learnability

    Aug 5, 2026Md Sadman Sakib Rahman, Che-Yung Shen, Aydogan OzcanDiffractOptical

  14. PLAN: Parallel Liquid-Inspired Approximation Network for Efficient Representation Learning in Flexible Job Shop Scheduling

    Aug 4, 2026Dhivya Dharshini Kannan, Wei Zhang, Jieyi Bi +5Flexible Job-Shop SchedulingNeural-Network Approximation

  15. Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

    Aug 3, 2026Harris Cobb, Wenbo Hao, Yingjie LiuDerivative PricingNeural-Network Approximation

  16. Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View

    Aug 2, 2026Tong Mao, Jinchao XuNeural-Network Approximation

  17. Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural-Network ApproximationRegularity

  18. Error Analysis of Neural-Network-Based Engression

    Jul 30, 2026Juntong Chen, Zijian Guo, Xinwei ShenNeural-Network ApproximationEqual Error Rate

  19. Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes

    Jul 29, 2026Lennon J. Shikhman, Michael Galarnyk, Aadi Dash +1Derivative PricingNeural-Network Approximation

  20. Universality and Approximation Rates of Graph Neural Networks with Random Features

    Jul 29, 2026Lukas Gonon, Thilo Meyer-Brandis, Niklas WeberGraph Neural NetworksNeural-Network Approximation

  21. Operator Neural Jump ODEs: L^2-optimal prediction in function spaces

    Jul 25, 2026Florian Krach, Oliver Löthgren, Josef TeichmannNeural Ordinary Differential EquationsNeural-Network Approximation

  22. From Score Approximation to Distribution Approximation in Score-Based Diffusion Models

    Jul 24, 2026Lan V. TruongScore-Based Diffusion ModelNeural-Network Approximation

  23. Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H^2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

    Jul 21, 2026Nathanael Tepakbong, Jun Fan, Xiang Zhou +1Neural-Network ApproximationApproximation Algorithms

  24. Functional Equivalence and Geometric Diversity in Neural Network Approximations: An Empirical Characterization

    Jul 21, 2026Anuragine S A, Prem JagadeesanNeural-Network ApproximationIdentifiability

  25. Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

    Jul 17, 2026Ronald KatendeMultiscale DynamicsPartial Differential Equations

  26. NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

    Jul 15, 2026Anastasis Kratsios, Giulia Livieri, Philipp SchmockerNeural-Network ApproximationStochastic Processes

  27. Approximation of solutions of parameter-dependent problems by residual neural networks

    Jul 15, 2026Ana CarpioNeural-Network ApproximationEuler Discretization

  28. Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems

    Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3Multiscale DynamicsNeural-Network Approximation

  29. An optimal control approach for neural network architecture adaptation with a posteriori error estimation

    Jul 8, 2026C G Krishnanunni, Thomas Scott, Tan Bui-ThanhNeural-Network ApproximationNeural Network Optimization

  30. On Explicit Super-Expressive Approximation for Neural Networks

    Jul 7, 2026Feng-Lei Fan, Ze-Yu Li, Chen-Yu Wang +1Neural-Network ApproximationLipschitz Constant

  31. A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems

    Jul 7, 2026Fabian Schneider, Tapio Helin, Leila TaghizadehIll-Posed Inverse ProblemNeural-Network Approximation

  32. From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators

    Jul 1, 2026Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan WaniorekFourier Neural OperatorsNeural Operators

  33. Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains

    Jun 30, 2026Haixin Wang, Haoning Dang, Fei Wang +1Partial Differential EquationsSolution Operator

  34. A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch

    Jun 28, 2026Xichuan ZhangStochastic Differential EquationsNeural-Network Approximation

  35. Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation

    Jun 25, 2026Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim +2Neural-Network ApproximationArtificial Neural Networks

  36. A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

    Jun 23, 2026Yanwei Jia, Du Ouyang, Huyên Pham +1Partial Differential EquationsDifferentiable Programming

  37. EML Trees Are Universal Approximators

    Jun 22, 2026Joe Germany, Elie Abdo, Joseph BakarjiNeural-Network ApproximationTrees

  38. Recurrent neural networks approximate continuous functions

    Jun 18, 2026Valentin Abadie, Clemens Hutter, Helmut BölcskeiNeural-Network ApproximationRecurrent Neural Networks

  39. A fast direct solver based neural network for solving PDEs

    Jun 18, 2026Jashwanth Reddy Kadaru, Vaishnavi GujjulaNeural Partial Differential Equation SolversPartial Differential Equations

  40. Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structures

    Jun 18, 2026Xinhe Mu, Zaijiu Shang, Zhaoqi Zhou +4Score-Based Diffusion ModelLow-Dimensional Structure

  41. Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

    Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Probabilistic Operator LearningRegularity

  42. Finsler Geometry, Graph Neural Networks, and You

    Jun 15, 2026T. Mitchell Roddenberry, Richard G. BaraniukGraph LaplaciansRiemannian Manifolds

  43. Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

    Jun 15, 2026Baicheng Li, Haizhao Yang, Shijun ZhangNeural-Network ApproximationActivation Functions

  44. Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

    Jun 10, 2026Ismail Huseynov, Arzu Ahmadova, Agamirza BashirovPhysics-Informed Neural Network FrameworkInequality Constraints

  45. SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators

    Jun 9, 2026Pengqing Shi, Jie Yin, Stephen Tierney +1Fourier Neural OperatorsNeural Operators

  46. Convergence Rates for Neural-Network Estimation with Current-Status Data

    Jun 8, 2026Yuan Wu, Tianhui ZhouNeural-Network ApproximationOptimization Convergence Analysis

  47. Weighted universal approximation of differentiable maps on infinite-dimensional manifolds

    Jun 8, 2026Philipp Schmocker, Josef TeichmannNeural-Network ApproximationActivation Functions

  48. Fourier Neural Operators with rank-1 lattice points and hyperbolic cross

    Jun 7, 2026Jakob Dilen, Alexander Keller, Frances Y. Kuo +1Fourier Neural OperatorsFourier

  49. Compositional Approximation Can Strictly Outperform Superpositional Approximation

    Jun 7, 2026Dennis Elbrächter, Philipp PetersenNeural-Network ApproximationApproximation Algorithms

  50. Where the Score Lives: A Wavelet View of Diffusion

    Jun 6, 2026Emma Finn, Binxu Wang, T. Anderson Keller +1Score-Based Diffusion ModelDiscrete Wavelet Transform

  51. Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning

    Jun 1, 2026Mingtao Xia, Qijing ShenRadial Basis FunctionKolmogorov-Arnold Networks

  52. Variation Spaces for Encoder--Decoder Neural Operators: Approximation and Generalization

    May 31, 2026Jia-Qi Yang, Lei ShiNeural OperatorsNeural-Network Approximation

  53. Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

    May 29, 2026Qihong Yang, Qiaolin HeNeural Partial Differential Equation SolversPartial Differential Equations

  54. Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability

    May 26, 2026Zhong Zhang, Giacomo Acciarini, Dario Izzo +2Gradient-Based Trajectory OptimizationNeural-Network Approximation

  55. Random Neural Network Expressivity for Non-Linear Partial Differential Equations

    May 24, 2026Muhammed Ali Mehmood, Lukas GononPartial Differential EquationsNeural-Network Approximation

  56. IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients

    May 24, 2026Shan Zhong, George BirosFourier Neural OperatorsPartial Differential Equations

  57. Optimization of randomized neural networks for transfer operator approximation

    May 22, 2026Mohammad Tabish, Stefan KlusNeural-Network ApproximationNeural Network Optimization

  58. Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputs

    May 22, 2026Lucia CelliLarge Deviations TheoryNeural-Network Approximation

  59. Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations

    May 21, 2026Shuang Chen, Juncai He, Xue-Cheng TaiNeural OperatorsNeural-Network Approximation

  60. Approximation Theory for Neural Networks: Old and New

    May 20, 2026Soumendu Sundar Mukherjee, Himasish TalukdarNeural-Network ApproximationKolmogorov-Arnold Networks