Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
Fuente:
arXiv
Saved in:
| Main Authors: | Chen, Shuang, He, Juncai, Tai, Xue-Cheng |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
A Low Rank Neural Representation of Entropy Solutions
by: Rim, Donsub, et al.
Published: (2024)
by: Rim, Donsub, et al.
Published: (2024)
Time-Frequency Analysis for Neural Networks
by: Abdeljawad, Ahmed, et al.
Published: (2025)
by: Abdeljawad, Ahmed, et al.
Published: (2025)
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
by: Li, Ziqian, et al.
Published: (2024)
by: Li, Ziqian, et al.
Published: (2024)
A theoretical analysis on the inversion of matrices via Neural Networks designed with Strassen algorithm
by: Romera, Gonzalo, et al.
Published: (2025)
by: Romera, Gonzalo, et al.
Published: (2025)
SUPN: Shallow Universal Polynomial Networks
by: Morrow, Zachary, et al.
Published: (2025)
by: Morrow, Zachary, et al.
Published: (2025)
Approximation and Gradient Descent Training with Neural Networks
by: Welper, G.
Published: (2024)
by: Welper, G.
Published: (2024)
Enhancing Future Prediction of Linear and Nonlinear Reduced-Order Models for Transport-Dominated Problems Using Lagrangian Data
by: Li, Meng, et al.
Published: (2026)
by: Li, Meng, et al.
Published: (2026)
A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks
by: Chen, Shi, et al.
Published: (2021)
by: Chen, Shi, et al.
Published: (2021)
Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
by: Yao, Boyuan, et al.
Published: (2025)
by: Yao, Boyuan, et al.
Published: (2025)
Discretization Error of Fourier Neural Operators
by: Lanthaler, Samuel, et al.
Published: (2024)
by: Lanthaler, Samuel, et al.
Published: (2024)
Universal approximation property of ODENet and ResNet with a single activation function
by: Kimura, Masato, et al.
Published: (2024)
by: Kimura, Masato, et al.
Published: (2024)
PODNO: Proper Orthogonal Decomposition Neural Operators
by: Cheng, Zilan, et al.
Published: (2025)
by: Cheng, Zilan, et al.
Published: (2025)
Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications
by: Fabiani, Gianluca
Published: (2024)
by: Fabiani, Gianluca
Published: (2024)
Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation
by: Li, Li'ang, et al.
Published: (2023)
by: Li, Li'ang, et al.
Published: (2023)
Transformed Snapshot Interpolation with High Resolution Transforms
by: Welper, G.
Published: (2019)
by: Welper, G.
Published: (2019)
Neural empirical interpolation method for nonlinear model reduction
by: Hirsch, Max, et al.
Published: (2024)
by: Hirsch, Max, et al.
Published: (2024)
Near-best univariate spline discrete quasi-interpolants on non-uniform partitions
by: Barrera, D., et al.
Published: (2004)
by: Barrera, D., et al.
Published: (2004)
Optimal Compactly Supported Functions in Sobolev Spaces
by: Schaback, Robert
Published: (2024)
by: Schaback, Robert
Published: (2024)
Weights initialization of neural networks for function approximation
by: Hu, Xinwen, et al.
Published: (2025)
by: Hu, Xinwen, et al.
Published: (2025)
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks
by: Siegel, Jonathan W.
Published: (2023)
by: Siegel, Jonathan W.
Published: (2023)
Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's
by: Arakelyan, Avetik, et al.
Published: (2024)
by: Arakelyan, Avetik, et al.
Published: (2024)
Learning Contractive Integral Operators with Fredholm Integral Neural Operators
by: Georgiou, Kyriakos C., et al.
Published: (2026)
by: Georgiou, Kyriakos C., et al.
Published: (2026)
Entropy-based convergence rates of greedy algorithms
by: Li, Yuwen, et al.
Published: (2023)
by: Li, Yuwen, et al.
Published: (2023)
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators
by: Fabiani, Gianluca, et al.
Published: (2024)
by: Fabiani, Gianluca, et al.
Published: (2024)
Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness
by: Song, Lunji, et al.
Published: (2025)
by: Song, Lunji, et al.
Published: (2025)
A new analysis of empirical interpolation methods and Chebyshev greedy algorithms
by: Li, Yuwen
Published: (2024)
by: Li, Yuwen
Published: (2024)
Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs
by: Bi, Ran, et al.
Published: (2026)
by: Bi, Ran, et al.
Published: (2026)
An Optimal Weighted Least-Squares Method for Operator Learning
by: Turnage, John, et al.
Published: (2025)
by: Turnage, John, et al.
Published: (2025)
A Universal Approximation Theorem for Neural Networks with Outputs in Locally Convex Spaces
by: Saini, Sachin
Published: (2026)
by: Saini, Sachin
Published: (2026)
Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
by: Appella, Simone, et al.
Published: (2024)
by: Appella, Simone, et al.
Published: (2024)
Vanilla Feedforward Neural Networks as a Discretization of Dynamical Systems
by: Duan, Yifei, et al.
Published: (2022)
by: Duan, Yifei, et al.
Published: (2022)
Optimal recovery of linear operators from information of random functions
by: Osipenko, K. Yu.
Published: (2024)
by: Osipenko, K. Yu.
Published: (2024)
Taylor-Accelerated Neural Network Interpolation Operators on Irregular Grids with Higher Order Approximation
by: Saini, Sachin
Published: (2026)
by: Saini, Sachin
Published: (2026)
Improving Matrix Exponential for Generative AI Flows: A Taylor-Based Approach Beyond Paterson--Stockmeyer
by: Sastre, Jorge, et al.
Published: (2025)
by: Sastre, Jorge, et al.
Published: (2025)
Achieving Universal Approximation and Universal Interpolation via Nonlinearity of Control Families
by: Cai, Yongqiang, et al.
Published: (2025)
by: Cai, Yongqiang, et al.
Published: (2025)
Kantorovich--Kernel Neural Operators: Approximation Theory, Asymptotics, and Neural Network Interpretation
by: He, Tian-Xiao
Published: (2026)
by: He, Tian-Xiao
Published: (2026)
An iterative method for the solution of Laplace-like equations in high and very high space dimensions
by: Yserentant, Harry
Published: (2024)
by: Yserentant, Harry
Published: (2024)
Approximation Error and Complexity Bounds for ReLU Networks on Low-Regular Function Spaces
by: Davis, Owen, et al.
Published: (2024)
by: Davis, Owen, et al.
Published: (2024)
Best Approximations on Quasi-Cone Metric Spaces
by: Zakiyudin, Ahmad Hisbu, et al.
Published: (2025)
by: Zakiyudin, Ahmad Hisbu, et al.
Published: (2025)
Neural Network Operator-Based Fractal Approximation: Smoothness Preservation and Convergence Analysis
by: Bhat, Aaqib Ayoub, et al.
Published: (2025)
by: Bhat, Aaqib Ayoub, et al.
Published: (2025)
Similar Items
-
A Low Rank Neural Representation of Entropy Solutions
by: Rim, Donsub, et al.
Published: (2024) -
Time-Frequency Analysis for Neural Networks
by: Abdeljawad, Ahmed, et al.
Published: (2025) -
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
by: Li, Ziqian, et al.
Published: (2024) -
A theoretical analysis on the inversion of matrices via Neural Networks designed with Strassen algorithm
by: Romera, Gonzalo, et al.
Published: (2025) -
SUPN: Shallow Universal Polynomial Networks
by: Morrow, Zachary, et al.
Published: (2025)