Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | Yao, Boyuan, Luo, Dingcheng, Cao, Lianghao, Kovachki, Nikola, O'Leary-Roseberry, Thomas, Ghattas, Omar |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Performance of Neural and Polynomial Operator Surrogates
by: Westermann, Josephine, et al.
Published: (2026)
by: Westermann, Josephine, et al.
Published: (2026)
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)
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
by: Chen, Shuang, et al.
Published: (2026)
by: Chen, Shuang, et al.
Published: (2026)
Vanilla Feedforward Neural Networks as a Discretization of Dynamical Systems
by: Duan, Yifei, et al.
Published: (2022)
by: Duan, Yifei, et al.
Published: (2022)
Fourier Residual Networks Achieve Spectral Accuracy for Discontinuous Functions
by: Davis, Owen, et al.
Published: (2026)
by: Davis, Owen, et al.
Published: (2026)
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)
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)
Gaussian mixture Taylor approximations of risk measures constrained by PDEs with Gaussian random field inputs
by: Luo, Dingcheng, et al.
Published: (2024)
by: Luo, Dingcheng, et al.
Published: (2024)
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)
Discretization Error of Fourier Neural Operators
by: Lanthaler, Samuel, et al.
Published: (2024)
by: Lanthaler, Samuel, et al.
Published: (2024)
Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation
by: Ibrahim, Abdul Qadir, et al.
Published: (2024)
by: Ibrahim, Abdul Qadir, et al.
Published: (2024)
SUPN: Shallow Universal Polynomial Networks
by: Morrow, Zachary, et al.
Published: (2025)
by: Morrow, Zachary, et al.
Published: (2025)
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)
Data-Free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs
by: Lee, Jinsil, et al.
Published: (2025)
by: Lee, Jinsil, et al.
Published: (2025)
Multiscale Neural Networks for Approximating Green's Functions
by: Hao, Wenrui, et al.
Published: (2024)
by: Hao, Wenrui, et al.
Published: (2024)
Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
by: Haugen, Emil, et al.
Published: (2025)
by: Haugen, Emil, et al.
Published: (2025)
The Neural Approximated Virtual Element Method for Elasticity Problems
by: Berrone, Stefano, et al.
Published: (2025)
by: Berrone, Stefano, et al.
Published: (2025)
PODNO: Proper Orthogonal Decomposition Neural Operators
by: Cheng, Zilan, et al.
Published: (2025)
by: Cheng, Zilan, et al.
Published: (2025)
Neural Approximate Inverse Preconditioners
by: Xu, Tianshi, et al.
Published: (2025)
by: Xu, Tianshi, et al.
Published: (2025)
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)
Geometric Generalization of Neural Operators from Kernel Integral Perspective
by: Han, Mingyu, et al.
Published: (2026)
by: Han, Mingyu, et al.
Published: (2026)
A Minimal Control Family of Dynamical Systems for Universal Approximation
by: Duan, Yifei, et al.
Published: (2023)
by: Duan, Yifei, et al.
Published: (2023)
EGPT-PINN: Entropy-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conservation laws
by: Ji, Yajie, et al.
Published: (2025)
by: Ji, Yajie, et al.
Published: (2025)
A Low Rank Neural Representation of Entropy Solutions
by: Rim, Donsub, et al.
Published: (2024)
by: Rim, Donsub, et al.
Published: (2024)
Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
by: Sittoni, Pietro, et al.
Published: (2026)
by: Sittoni, Pietro, et al.
Published: (2026)
Discontinuous hybrid neural networks for the one-dimensional partial differential equations
by: Wang, Xiaoyu, et al.
Published: (2025)
by: Wang, Xiaoyu, et al.
Published: (2025)
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)
A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
by: Cao, Jiachuan, et al.
Published: (2026)
by: Cao, Jiachuan, et al.
Published: (2026)
Development and Analysis of Chien-Physics-Informed Neural Networks for Singular Perturbation Problems
by: Singh, Gautam, et al.
Published: (2025)
by: Singh, Gautam, et al.
Published: (2025)
Fast algorithms for interpolation with clamped $L$-splines of order four
by: Kounchev, O., et al.
Published: (2026)
by: Kounchev, O., et al.
Published: (2026)
LR B-spline perspective for RM B-splines: construction and effortless refinements
by: Patrizi, Francesco
Published: (2025)
by: Patrizi, Francesco
Published: (2025)
A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension
by: Lin, Ting, et al.
Published: (2026)
by: Lin, Ting, et al.
Published: (2026)
Quasi-interpolation projectors for Subdivision Surfaces
by: Xu, Hailun, et al.
Published: (2024)
by: Xu, Hailun, et al.
Published: (2024)
Element-based B-spline basis function spaces: construction and application in isogeometric analysis
by: Yang, Peng, et al.
Published: (2026)
by: Yang, Peng, et al.
Published: (2026)
Operator Inference for Elliptic Eigenvalue Problems
by: Li, Haoqian, et al.
Published: (2025)
by: Li, Haoqian, et al.
Published: (2025)
Accuracy and stability of Artificial Neural Networks for HP-Splines frequency parameter selection
by: Bruni, Vittoria, et al.
Published: (2026)
by: Bruni, Vittoria, et al.
Published: (2026)
Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networks
by: Tanaka, Kazuaki, et al.
Published: (2026)
by: Tanaka, Kazuaki, et al.
Published: (2026)
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)
Multilevel Training for Kolmogorov Arnold Networks
by: Southworth, Ben S., et al.
Published: (2026)
by: Southworth, Ben S., et al.
Published: (2026)
A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations
by: Yuan, Long, et al.
Published: (2025)
by: Yuan, Long, et al.
Published: (2025)
Similar Items
-
Performance of Neural and Polynomial Operator Surrogates
by: Westermann, Josephine, et al.
Published: (2026) -
Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation
by: Li, Li'ang, et al.
Published: (2023) -
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
by: Chen, Shuang, et al.
Published: (2026) -
Vanilla Feedforward Neural Networks as a Discretization of Dynamical Systems
by: Duan, Yifei, et al.
Published: (2022) -
Fourier Residual Networks Achieve Spectral Accuracy for Discontinuous Functions
by: Davis, Owen, et al.
Published: (2026)