1. Approximation Rates of Shallow Neural Networks: Barron Spaces, Activation Functions and Optimality Analysis
   2025/10/21 by Jian Lü, Lu, Jian, Xiaohuang Huang +1 · 1 citation
   Computer Science · Physics and Astronomy · #41A46 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
2. Kernel interpolation on generalized sparse grids
   2025/05/18 by Griebel, Michael, Harbrecht, Helmut, Multerer, Michael · 1 citation
   #41A46 #41A63 #46E35 #FOS: Mathematics #Numerical Analysis (math.NA)
3. Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains
   2024/11/06 by Abdeljawad, Ahmed, Dittrich, Thomas · 3 citations
   #41A25 #41A30 #41A46 #46E35 #62M45 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
4. Neural empirical interpolation method for nonlinear model reduction
   2024/06/05 by Max Hirsch, Federico Pichi, Hirsch, Max +3 · 3 citations
   Computer Science · Engineering · #41A05 #41A46 #65N22 #68T07 #76A15 #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA)
5. Twenty-five years of greedy bases
   2024/05/31 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +3 · 2 citations
   Chemistry · Environmental Science · #41A17 #41A46 #41A65 (Primary) 41A25 #46B15 (Secondary) #Chemistry and Chemical Engineering #FOS: Mathematics #Functional Analysis (math.FA) #History and advancements in chemistry
6. Structure-preserving neural networks in data-driven rheological models
   2024/01/13 by Nicola Parolini, Parolini, Nicola, Andrea Poiatti +5 · 2 citations
   Chemical Engineering · Engineering · Physics and Astronomy · #41A46 #76A05 #76D03 #76M10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies
7. Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces
   2023/12/13 by Ahmed Abdeljawad, Abdeljawad, Ahmed, Thomas Dittrich +1 · 1 citation
   Physics and Astronomy · #41A25 #41A30 #41A46 #46E35 #62M45 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
8. Local Randomized Neural Networks with Hybridized Discontinuous Petrov-Galerkin Methods for Stokes-Darcy Flows
   2023/12/10 by Dang, Haoning, Wang, Fei · 1 citation
   #41A46 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)
9. Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms
   2023/11/08 by Yang, Yahong, Lu, Yulong · 1 citation
   #41A25 #41A46 #65D07 #68Q25 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
10. Performance bounds for Reduced Order Models with Application to Parametric Transport
    2023/10/22 by Rim, D., Welper, G. · 1 citation
    #41A25 #41A46 #65N15 #FOS: Mathematics #Numerical Analysis (math.NA)
11. Spectral Barron space for deep neural network approximation
    2023/09/02 by Liao, Yulei, Ming, Pingbing · 5 citations
    #32C22 #32K05 #33C20 #41A25 #41A46 #42A38 #68T07 #FOS: Mathematics #Numerical Analysis (math.NA)
12. Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks
    2023/07/28 by Siegel, Jonathan W. · 2 citations
    #41A25 #41A46 #52A21 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
13. Compositional Sparsity, Approximation Classes, and Parametric Transport Equations
    2022/07/13 by Dahmen, Wolfgang · 4 citations
    #35A35 #35B30 #35L04 #41A25 #41A46 #41A63 #FOS: Mathematics #Numerical Analysis (math.NA)
14. Optimal Convergence Rates for the Orthogonal Greedy Algorithm
    2021/06/28 by Siegel, Jonathan W., Xu, Jinchao · 1 citation
    #41A25 #41A46 #46N30 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)
15. New parameters and Lebesgue-type estimates in greedy approximation
    2021/04/22 by Albiac, Fernando, Ansorena, Jose L., Berna, Pablo M. · 1 citation
    #41A17 #41A46 #41A65 (Primary) 41A25 #46B15 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
16. Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
    2021/04/06 by Grohs, Philipp, Voigtlaender, Felix · 2 citations
    #41A25 #41A46 #41A65 #65Y20 #68T05 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG)
17. Quantitative approximation results for complex-valued neural networks
    2021/02/25 by A. Caragea, Caragea, A., D. G. Lee +7 · 1 citation
    Computer Science · #41A25 #41A46 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy Logic and Control Systems #Machine Learning (cs.LG) #Machine Learning and ELM #Neural Networks and Applications
18. Neural network approximation and estimation of classifiers with classification boundary in a Barron class
    2020/11/18 by Caragea, Andrei, Petersen, Philipp, Voigtlaender, Felix · 2 citations
    #41A25 #41A46 #42B35 #46E15 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (stat.ML)
19. Error estimates of residual minimization using neural networks for linear PDEs
    2020/10/15 by Yeonjong Shin, Shin, Yeonjong, Zhongqiang Zhang +3 · 6 citations
    Engineering · Physics and Astronomy · #35J25 #35S15 #41A46 #65M12 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering
20. Sparse approximation of triangular transports. Part I: the finite dimensional case
    2020/06/12 by Zech, Jakob, Marzouk, Youssef · 1 citation
    #32D05 #41A10 #41A25 #41A46 #62D99 #65D15 #FOS: Mathematics #Numerical Analysis (math.NA) #Statistics Theory (math.ST)
21. Efficient Approximation of Solutions of Parametric Linear Transport\n Equations by ReLU DNNs
    2020/01/30 by Fabian Laakmann, Philipp Petersen, Laakmann, Fabian +1 · 1 citation
    Engineering · Physics and Astronomy · #35A35 #35Q49 #41A25 #41A46 #65N30 #68T05 #Analysis of PDEs (math.AP) #Energy Load and Power Forecasting #FOS: Mathematics #Functional Analysis (math.FA) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
22. Strong partially greedy bases and Lebesgue-type inequalities
    2020/01/05 by Berasategui, Miguel, Berná, Pablo M., Lassalle, Silvia · 2 citations
    #41A17 #41A46 #41A65 #46B15 #46B45 #FOS: Mathematics #Functional Analysis (math.FA)
23. Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems
    2019/12/30 by Donsub Rim, Rim, Donsub, Benjamin Peherstorfer +3 · 3 citations
    Engineering · Mathematics · Physics and Astronomy · #35F20 #41A46 #78M12 #78M34 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
24. Universal Approximation with Deep Narrow Networks
    2019/05/21 by Kidger, Patrick, Lyons, Terry · 12 citations
    #41A46 #41A63 #68T07 #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML)
25. Nonlinear Approximation and (Deep) ReLU Networks
    2019/05/05 by Daubechies, I., DeVore, R., Foucart, S. +2 · 1 citation
    #41A25 #41A30 #41A46 #68T99 #82C32 #92B20 #FOS: Computer and information sciences #Machine Learning (cs.LG)
26. A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
    2019/03/31 by Kutyniok, Gitta, Petersen, Philipp, Raslan, Mones +1 · 6 citations
    #35A35 #35J99 #41A25 #41A46 #65N30 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
27. Decay of the Kolmogorov N-width for wave problems
    2019/03/20 by Constantin Greif, Greif, Constantin, Karsten Urban +1 · 7 citations
    Engineering · Mathematics · #41A46 #65D15 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
28. Tensor network ranks
    2018/01/08 by Ye, Ke, Lim, Lek-Heng · 1 citation
    #15A69 #41A30 #41A46 #41A65 #45L05 #65C60 #81P50 #81Q05 #FOS: Mathematics #Numerical Analysis (math.NA)
29. Optimal approximation of piecewise smooth functions using deep ReLU neural networks
    2017/09/15 by Petersen, Philipp, Voigtlaender, Felix · 13 citations
    #41A10 #41A25 #41A46 #68T05 #82C32 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
30. Optimal Approximation with Sparsely Connected Deep Neural Networks
    2017/05/04 by Bölcskei, Helmut, Grohs, Philipp, Kutyniok, Gitta +1 · 6 citations
    #41A25 #41A46 #42C15 #42C40 #68T05 #82C32 #94A12 #94A34 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Machine Learning (cs.LG)

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