Cover Image

Fourier Neural Operators for Non-Markovian Processes:Approximation Theorems and Experiments

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Lee, Wonjae, Kim, Taeyoung, Park, Hyungbin
Format:	Preprint
Published:	2025
Subjects:	Machine Learning Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws
by: Kim, Taeyoung, et al.
Published: (2024)

Two-grid Penalty Approximation Scheme for Doubly Reflected BSDEs
by: Lee, Wonjae, et al.
Published: (2026)

Universal Approximation of Operators with Transformers and Neural Integral Operators
by: Zappala, Emanuele, et al.
Published: (2024)

Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
by: Li, Zongyi, et al.
Published: (2022)

Component Fourier Neural Operator for Singularly Perturbed Differential Equations
by: Li, Ye, et al.
Published: (2024)

Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains
by: Lingsch, Levi, et al.
Published: (2023)

Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations
by: Furuya, Takashi, et al.
Published: (2024)

Guaranteed Approximation Bounds for Mixed-Precision Neural Operators
by: Tu, Renbo, et al.
Published: (2023)

Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators
by: Pellegrini, Luca, et al.
Published: (2025)

Operator SVD with Neural Networks via Nested Low-Rank Approximation
by: Ryu, J. Jon, et al.
Published: (2024)

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks
by: Gleyzer, Sergei, et al.
Published: (2025)

Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media
by: Cai, Yiyang, et al.
Published: (2026)

Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration
by: Kim, Hwanwoo, et al.
Published: (2024)

Preconditioned Additive Gaussian Processes with Fourier Acceleration
by: Wagner, Theresa, et al.
Published: (2025)

Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations
by: Kim, Chanyoung, et al.
Published: (2026)

Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
by: Subedi, Unique, et al.
Published: (2024)

Parareal Neural Networks Emulating a Parallel-in-time Algorithm
by: Lee, Chang-Ock, et al.
Published: (2021)

Multigrade Neural Network Approximation
by: Zhang, Shijun, et al.
Published: (2026)

Physics-embedded Fourier Neural Network for Partial Differential Equations
by: Xu, Qingsong, et al.
Published: (2024)

MODNO: Multi Operator Learning With Distributed Neural Operators
by: Zhang, Zecheng
Published: (2024)

Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
by: Lee, Jonghyeon, et al.
Published: (2024)

Continuum Attention for Neural Operators
by: Calvello, Edoardo, et al.
Published: (2024)

Enhancing Solutions for Complex PDEs: Introducing Complementary Convolution and Equivariant Attention in Fourier Neural Operators
by: Zhao, Xuanle, et al.
Published: (2023)

Non-Asymptotic Stability and Consistency Guarantees for Physics-Informed Neural Networks via Coercive Operator Analysis
by: Katende, Ronald
Published: (2025)

A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory
by: Weihs, Adrien, et al.
Published: (2025)

Approximation with SiLU Networks: Constant Depth and Exponential Rates for Basic Operations
by: Ayena, Koffi O.
Published: (2025)

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery
by: Liu, Ning, et al.
Published: (2025)

U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics
by: Ma, Yingzhe, et al.
Published: (2026)

Physics-Informed Geometry-Aware Neural Operator
by: Zhong, Weiheng, et al.
Published: (2024)

A Mathematical Analysis of Neural Operator Behaviors
by: Le, Vu-Anh, et al.
Published: (2024)

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
by: Lowery, Matthew, et al.
Published: (2024)

Approximation Power of Deep Neural Networks: an explanatory mathematical survey
by: Davis, Owen, et al.
Published: (2022)

Multi-Level Monte Carlo Training of Neural Operators
by: Rowbottom, James, et al.
Published: (2025)

Revisiting Orbital Minimization Method for Neural Operator Decomposition
by: Ryu, J. Jon, et al.
Published: (2025)

Neural Operator: Learning Maps Between Function Spaces
by: Kovachki, Nikola, et al.
Published: (2021)

On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions
by: Lu, Yulong, et al.
Published: (2025)

HyperNOs: Automated and Parallel Library for Neural Operators Research
by: Ghiotto, Massimiliano
Published: (2025)

Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
by: Wang, Tian, et al.
Published: (2024)

HAMLET: Graph Transformer Neural Operator for Partial Differential Equations
by: Bryutkin, Andrey, et al.
Published: (2024)

Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers
by: Zhang, Enrui, et al.
Published: (2022)