18 citations · 39 across the 7 of their papers we have counts for
7 papers
Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems
Xiu Yang, Li-Lian Wang, Huiyuan Li +1
In this paper, we introduce a new family of orthogonal systems, termed as the Müntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\|x\|^{2θ+2μ…
Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator
Bian Li, Hanchen Wang, Shihang Feng +2
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial d…
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems
Yiming Fan, Xiaochuan Tian, Xiu Yang +3
In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media. In parti…
A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems
Zhiwei Fang, Justin Zhang, Xiu Yang
In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the su…
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
Yixiang Deng, Guang Lin, Xiu Yang
We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its g…
Nonnegativity-Enforced Gaussian Process Regression
Andrew Pensoneault, Xiu Yang, Xueyu Zhu
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical prop…