Neural Approximations

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10 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

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  1. FOSLS-deRhaNN: native de Rham neural classes for H(div) and H(curl) with applications to first-order system least-squares neural network methods for partial differential equations

    Oct 6, 2026Shun ZhangNeural ApproximationsNeural Fields

    Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong, China

  2. Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation

    Sep 30, 2026J. H. Ramirez-GonzalezStochastic Differential EquationsTime Discretization

    Institute of Mathematics and Statistics, University of São Paulo (IME–USP), São Paulo, Brazil

  3. Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics

    Sep 30, 2026Mauricio Herrera-MarínFourier Neural OperatorsNeural Operators

    Facultad de Ingenier´ıa, Universidad del Desarrollo, Santiago, Chile

  4. Arbitrary-Accuracy Neural Approximation with Optimal Neuron Count and Near-Optimal Bit Complexity

    Sep 28, 2026Zilan Cheng, Li-Lian Wang, Zhongjian WangNeural ApproximationsApproximation

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore.

  5. From Distributions to Stochastic Processes: Neural Approximation of Measure-Valued Maps

    Sep 27, 2026Yichen Wang, Ziyi Wang, Wenlian Lu +5Probability MeasuresStochastic Processes

    Shanghai Center for Mathematical Sciences, Shanghai, China · Department of Mathematics, Fudan University, Shanghai, China · Center for Applied Mathematics, Fudan University, Shanghai, China +2

  6. AFT Neural Function Approximators for 1D Nonlinear Force Laws

    Sep 24, 2026Miriam Goldack, Johann Groß, Malte Krack +1Nonlinear DynamicsFinite Element Method

    Technische Universität Berlin, Chair of Cyber-Physical Systems in Mechanical Engineering, Straße des 17. Juni 135, 10623 Berlin, Germany · University of Stuttgart, Institute of Aircraft Propulsion Systems, Pfaffenwaldring 6, 70569 Stuttgart, Germany

  7. Neural Approximation by Function Composition: Rigidity and Doubly Exponential Convergence

    Sep 22, 2026Wentao Huang, Haizhang ZhangNeural ApproximationsApproximation

    Department of Mathematics, The University of Hong Kong, Hong Kong, P.R. China. · School of Mathematics, Sun Yat-sen University, Guangzhou, P.R. China.

  8. Optimal Tradeoffs Between Network Size and Parameter Magnitude in Neural Approximation and Minimax Regression

    Sep 22, 2026Baicheng Li, Zuowei Shen, Haizhao Yang +1Neural ApproximationsApproximation

    Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA. · Department of Mathematics, National University of Singapore, Singapore 119076. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.

  9. Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers

    Sep 17, 2026Nilo Schwencke, Roland MaierVariational FormulationNeural Partial Differential Equation Solvers

  10. Learning Lyapunov Operators for Nonlinear Systems

    Sep 16, 2026Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1Fourier Neural OperatorsNonlinear Dynamics

    Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

  11. Approximating Smooth Functionals with ReLU Networks

    Sep 14, 2026Shuhao JiaoNeural ApproximationsRectified Linear Unit Networks

    Department of Biostatistics, City University of Hong Kong, Hong Kong SAR, China.

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

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaResidual NetworksNeural Approximations

    Department of Applied Mathematics, University of Freiburg, Germany

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

    Aug 31, 2026Shijun ZhangNeural ApproximationsApproximation

    Department of Applied Mathematics Hong Kong Polytechnic University

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

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

  15. Reference-free logged energy-oracle recovery for neural approximations of symmetric coercive variational problems: conforming Riesz reconstruction and archive-level selection

    Aug 17, 2026Karim Bounja, Lahcen Laayouni, Boujemaa Achchab +1Reconstruction ErrorNeural Approximations

    Laboratory for Analysis and Modeling of Systems and Decision Support (LAMSAD), Hassan 1st University of Settat, Settat 26000, Morocco. · Department of Computer Science, School of Science and Engineering, Al Akhawayn University in Ifrane, Ifrane 53000, Morocco.

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

    Aug 10, 2026Konrad Kleinberg, Thomas KruseStochastic Differential EquationsNeural Approximations

    Department of Mathematics & Informatics, University of Wuppertal, Germany

  17. Approximation Rates for Metaplectic Neural Networks

    Aug 9, 2026Ahmed Abdeljawad, Marcello Carioni, Elena CorderoNeural ApproximationsNeural Network

    Johann Radon Institute of Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences Altenberger Straße 69, A-4040 Linz, Austria · Department of Applied Mathematics University of Twente 7500AE Enschede, The Netherlands · Dipartimento di Matematica Università degli Studi di Torino via Carlo Alberto 10, 10123 Torino, Italy

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

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

    Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden. · Digital Futures, Sweden. · Grenoble INP – Ensimag, Université Grenoble Alpes, Grenoble, France. +1

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

    Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural ApproximationsSpectral Representation Method

    School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China · Shenzhen Loop Area Institute, Shenzhen 518000, P. R. China

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

    Aug 5, 2026Khemraj Shukla, George Em KarniadakisFourier Neural OperatorsReynolds-Averaged Navier-Stokes

    Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA

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

    Aug 4, 2026Dhivya Dharshini Kannan, Wei Zhang, Jieyi Bi +5Job Shop SchedulingNeural Approximations

    Singapore Institute of Technology (SIT) · Nanyang Technological University (NTU) · Shanghai Jiao Tong University +1

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

    Aug 2, 2026Tong Mao, Jinchao XuNeural ApproximationsApproximation

    King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia

  23. Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural ApproximationsPartial Differential Equations

  24. Error Analysis of Neural-Network-Based Engression

    Jul 30, 2026Juntong Chen, Zijian Guo, Xinwei ShenNeural ApproximationsEqual Error Rate

    School of Mathematical Sciences, Xiamen University · Center for Data Science, Zhejiang University · Department of Statistics, University of Washington

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

    Jul 29, 2026Lukas Gonon, Thilo Meyer-Brandis, Niklas WeberGraph Neural NetworksAtom-Averaged Features

    School of Computer Science University of St. Gallen St. Gallen, 9000, Switzerland · Department of Mathematics LMU Munich Munich, 80333, Germany

  26. Operator Neural Jump ODEs: L2L^2-optimal prediction in function spaces

    Jul 25, 2026Florian Krach, Oliver Löthgren, Josef TeichmannNeural Ordinary Differential EquationsNeural Approximations

    Department of Mathematics ETH Zurich

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

    Jul 24, 2026Lan V. TruongScore-Based Diffusion ModelDiffusion Models

    Faculty of Computer Science and Engineering · Ho Chi Minh City University of Technology (HCMUT) · Vietnam National University Ho Chi Minh City (VNU-HCM), Vietnam

  28. Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H2(Ω)H^2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

    Jul 21, 2026Nathanael Tepakbong, Jun Fan, Xiang Zhou +1Parametric Physics-Informed Neural NetworkNeural Approximations

    Department of Data Science, City University of Hong Kong · Department of Mathematics, Hong Kong Baptist University · Department of Mathematics, City University of Hong Kong +1

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

    Jul 21, 2026Anuragine S A, Prem JagadeesanNeural ApproximationsApproximation

    Amrita School of Artificial Intelligence Amrita Vishwa Vidyapeetham, Coimbatore, India

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

    Jul 17, 2026Ronald KatendeVariationalMultiscale Dynamics

    Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda

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

    Jul 15, 2026Anastasis Kratsios, Giulia Livieri, Philipp SchmockerNeural ApproximationsStochastic Differential Equations

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

    Jul 15, 2026Ana CarpioNeural ApproximationsNeural Ordinary Differential Equations

    Universidad Complutense de Madrid, Spain

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

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

    Department of Aerospace Engineering & Engineering Mechanics, UT Austin · Oden Institute for Computational Engineering and Sciences, UT Austin.

  34. On Explicit Super-Expressive Approximation for Neural Networks

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

    Department of Data Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong. · Department of Mathematics, Chinese University of Hong Kong, University Avenue, Shatin, N.T., Hong Kong. · School of Civil Engineering and Architecture, Guangxi Minzu University, Nanning 530006, China.

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

    Jul 7, 2026Fabian Schneider, Tapio Helin, Leila TaghizadehBayesian Inverse ProblemsNeural Approximations

    Institute of Analysis and Scientific Computing, TU Wien, Vienna, Austria · School of Engineering Sciences, LUT University, Lappeenranta, Finland

  36. Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

    Jul 6, 2026Qi Zhou, Xuan Zhou, Xiao-Song YangNeural ApproximationsResidual Networks

    School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, P.R. China. · Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, P.R. China.

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

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

    University of Chicago

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

    Jun 28, 2026Xichuan ZhangStochastic Differential EquationsNeural Approximations

    Intelligent Game and Decision Lab, Beijing 100091, China

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

    Jun 25, 2026Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim +2Neural ApproximationsApproximation

    McMaster University & Vector Institute, Toronto, ON, Canada · Concordia University, Montréal, QC, Canada · University of Tokyo, Tokyo, Japan +2

  40. EML Trees Are Universal Approximators

    Jun 22, 2026Joe Germany, Elie Abdo, Joseph BakarjiNeural ApproximationsApproximation

    Department of Mathematics American University of Beirut Beirut, Lebanon · Department of Mechanical Engineering American University of Beirut Beirut, Lebanon

  41. Recurrent neural networks approximate continuous functions

    Jun 18, 2026Valentin Abadie, Clemens Hutter, Helmut BölcskeiNeural ApproximationsRecurrent Neural Networks

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

    Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Probabilistic Operator LearningLogarithmic Sobolev Inequalities

    School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, USA. · Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA. · Department of Mathematics, Hong Kong Baptist University, FSC1202, Fong Shu Chuen Building, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

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

    Jun 15, 2026Baicheng Li, Haizhao Yang, Shijun ZhangNeural ApproximationsLogarithmic Sobolev Inequalities

    Department of Mathematics, University of Maryland, College Park, MD, USA · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

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

    Jun 8, 2026Yuan Wu, Tianhui ZhouMaximum LikelihoodNeural Approximations

    Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA

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

    Jun 8, 2026Philipp Schmocker, Josef TeichmannNeural ApproximationsApproximation

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

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

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

    Jun 6, 2026Emma Finn, Binxu Wang, T. Anderson Keller +1Score-Based Diffusion ModelDiffusion Models

    The Kempner Instutite for the Study of Natural and Artificial Intelligence Harvard University, Cambridge, MA 15213

  48. Shortcomings and capacities of real-constrained neural networks in complex spaces

    Jun 3, 2026Andrew GracykNeural ApproximationsKernel Hilbert Spaces

    Department of Mathematics Purdue University West Lafayette, IN 47907, United States

  49. 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

    University of Houston, Philip Guthrie Hoffman Hall, 3551 Cullen Blvd, Houston, 77204, Texas, United States of America · University of Birmingham, Watson Building, Birmingham, B15 2TT,, United Kingdom · University of Oxford, Henry Wellcome Building for Molecular Physiology, Old Road, Oxford, OX3 7BN, Oxfordshire, United Kingdom

  50. Neural Network Compression by Approximate Differential Equivalence

    May 31, 2026Ravi Dhiman, Andrea Passarella, Mirco Tribastone +1Compressed ModelNeural Approximations

    IMT School for Advanced Studies Lucca 55100, Italy · IIT CNR, Pisa 56124, Italy

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

    May 31, 2026Jia-Qi Yang, Lei ShiNeural OperatorsNonlinear Operators

    School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.

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

    May 24, 2026Muhammed Ali Mehmood, Lukas GononPartial Differential EquationsNeural Approximations

    Department of Mathematics Imperial College London UK · School of Computer Science University of St. Gallen Switzerland

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

    May 24, 2026Shan Zhong, George BirosFourier Neural OperatorsAlgebraic Multigrid

    Oden Institute for Computational Science and Engineering, The University of Texas at Austin, 201 E 24th St, Austin, 78712, TX, USA · Walker Department of Mechanical Engineering, The University of Texas at Austin, 3012026 E Dean Keeton St, Austin, 78712, TX, USA

  54. Optimization of randomized neural networks for transfer operator approximation

    May 22, 2026Mohammad Tabish, Stefan KlusNeural ApproximationsNeural Network Optimization

    Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University, Edinburgh, UK · School of Mathematical & Computer Sciences, Heriot–Watt University, Edinburgh, UK

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

    May 22, 2026Lucia CelliNeural ApproximationsLarge Deviation Principle

    Department of Mathematics, University of Luxembourg

  56. Holographic functions and neural networks

    May 21, 2026Balazs SzegedyHolographic Reduced RepresentationsNeural Approximations

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

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

    Qiuzhen College, Tsinghua University, Haidian District, Beijing 100084, China · Yau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing 100084, China · Norwegian Research Center, Fantoftvegen 38, 5072 Bergen, Norway

  58. Approximation Theory for Neural Networks: Old and New

    May 20, 2026Soumendu Sundar Mukherjee, Himasish TalukdarNeural ApproximationsApproximation

    Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata

  59. Learning Orthonormal Bases for Function Spaces

    May 19, 2026Hamidreza Kamkari, Mohammad Sina Nabizadeh, Justin SolomonBasis FunctionsOrthogonality

    MIT CSAIL Cambridge, MA

  60. Stability and Discretization Error of State Space Model Neural Operators

    May 17, 2026Abderrahim Bendahi, Adrien Fradin, Johan Peralez +2Neural OperatorsFourier Neural Operators

    École polytechnique Paris, France · Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007 Villeurbanne, France · CNRS, UniversitéJulieLyonDigne1, INSA Lyon, LIRIS Lyon, France +1