9 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…