Cover Image

Sparse RBF Networks for PDEs and nonlocal equations: function space theory, operator calculus, and training algorithms

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Shao, Zihan, Pieper, Konstantin, Tian, Xiaochuan
Format:	Preprint
Published:	2026
Subjects:	Numerical Analysis Machine Learning
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Solving Nonlinear PDEs with Sparse Radial Basis Function Networks
by: Shao, Zihan, et al.
Published: (2025)

Nonuniform random feature models using derivative information
by: Pieper, Konstantin, et al.
Published: (2024)

Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning
by: Chiu, Shao-Ting, et al.
Published: (2026)

Resolution invariant deep operator network for PDEs with complex geometries
by: Huang, Jianguo, et al.
Published: (2024)

Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations
by: Xu, Tengfei, et al.
Published: (2023)

Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
by: Dang, Zhenhua, et al.
Published: (2026)

Learning solution operators of PDEs defined on varying domains via MIONet
by: Xiao, Shanshan, et al.
Published: (2024)

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

Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis
by: Tian, Xiaochuan, et al.
Published: (2023)

Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
by: Hong, Youngjoon, et al.
Published: (2024)

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
by: Dai, Chen-Yang, et al.
Published: (2026)

PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs
by: Brivio, Simone, et al.
Published: (2024)

Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs
by: Baba, Zakaria, et al.
Published: (2026)

A randomized algorithm to solve reduced rank operator regression
by: Turri, Giacomo, et al.
Published: (2023)

Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions
by: Wang, Jihong, et al.
Published: (2025)

Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
by: Baptista, Ricardo, et al.
Published: (2025)

Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems
by: Chenaud, Marien, et al.
Published: (2024)

Orthogonal greedy algorithm for linear operator learning with shallow neural network
by: Lin, Ye, et al.
Published: (2025)

VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior
by: Ko, Seungchan, et al.
Published: (2024)

Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
by: Yang, You, et al.
Published: (2026)

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs
by: Tomada, Lorenzo, et al.
Published: (2026)

Sequential decoder training for improved latent space dynamics identification
by: Anderson, William, 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)

Structure-preserving learning for multi-symplectic PDEs
by: Yıldız, Süleyman, et al.
Published: (2024)

CONFIDE: Contextual Finite Differences Modelling of PDEs
by: Linial, Ori, et al.
Published: (2023)

Solving PDEs on Unknown Manifolds with Machine Learning
by: Liang, Senwei, et al.
Published: (2021)

Neural Measures for learning distributions of Random PDEs
by: Arampatzis, Georgios, et al.
Published: (2025)

Sparse discovery of differential equations based on multi-fidelity Gaussian process
by: Meng, Yuhuang, et al.
Published: (2024)

Optimal deep learning of holomorphic operators between Banach spaces
by: Adcock, Ben, et al.
Published: (2024)

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
by: Jentzen, Arnulf, et al.
Published: (2023)

Physics-informed neural networks for operator equations with stochastic data
by: Escapil-Inchauspé, Paul, et al.
Published: (2022)

Dilated convolution neural operator for multiscale partial differential equations
by: Xu, Bo, et al.
Published: (2024)

Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristics
by: Dang, Haoning, et al.
Published: (2026)

Parameterized Physics-informed Neural Networks for Parameterized PDEs
by: Cho, Woojin, et al.
Published: (2024)

Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
by: Benitez, J. Antonio Lara, et al.
Published: (2023)

One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs
by: Auroy, Samuel, et al.
Published: (2025)

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

Transolver: A Fast Transformer Solver for PDEs on General Geometries
by: Wu, Haixu, et al.
Published: (2024)

Causality and Bayesian network PDEs for multiscale representations of porous media
by: Um, Kimoon, et al.
Published: (2019)

Multilevel CNNs for Parametric PDEs based on Adaptive Finite Elements
by: Schütte, Janina Enrica, et al.
Published: (2024)