4 citations · 4 across the 10 of their papers we have counts for
10 papers
Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains
Haixin Wang, Haoning Dang, Fei Wang +1
Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods oft…
Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification
Zirui Deng, Jingbo Sun, Deyu Meng +1
Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-co…
Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps
Chenhui Zhu, Fei Wang
We study operator learning for random obstacle-to-solution maps arising from elliptic variational inequalities with finite-band self-affine random obstacle fields. Instead of intro…
Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind
Chenhui Zhu, Fei Wang, Weimin Han
This paper presents a numerical approach to the stochastic obstacle problem using the stochastic Galerkin (SG) method. Due to the low regularity of the solution, linear finite elem…
Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
You Yang, Fei Wang
Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve ove…
Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces
Jingbo Sun, Fei Wang
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due t…
Structure-preserving Randomized Neural Networks for Incompressible Magnetohydrodynamics Equations
Yunlong Li, Fei Wang, Lingxiao Li
The incompressible magnetohydrodynamic (MHD) equations are fundamental in many scientific and engineering applications. However, their strong nonlinearity and dual divergence-free…
Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristics
Haoning Dang, Shi Jin, Fei Wang
This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics,…
Adaptive-Growth Randomized Neural Networks for PDEs: Algorithms and Numerical Analysis
Haoning Dang, Fei Wang, Song Jiang
Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initiali…
Local Randomized Neural Networks with Hybridized Discontinuous Petrov-Galerkin Methods for Stokes-Darcy Flows
Haoning Dang, Fei Wang
This paper introduces a new numerical approach that integrates local randomized neural networks (LRNNs) and the hybridized discontinuous Petrov-Galerkin (HDPG) method for solving c…