5 citations · 8 across the 12 of their papers we have counts for
14 papers
Spectral Barron spaces of periodic functions
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces are Fourier-Lebesgue-type spaces that arise in the approximation of functions by neural networks. Conventional spectral Barron spaces are mostly considered o…
Heat equations in spectral Barron spaces
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces, characterized by an \(L^1\)-based Fourier-Lebesgue norm, have earned significant attention in approximation theory due to their remarkable capacity to repre…
Inverse Geometric Diffraction by a Cone
Gang Bao, Xi Chen, Shuai Lu +1
Consider the inverse problem of recovering a strictly convex conical obstacle in from the diffraction coefficients along with arrival directions (lens data) or arriv…
Inverse Scattering by Diffracted Waves
Gang Bao, Xi Chen, Shuai Lu +1
In addition to reflection and refraction, another form of wave deviation is defined as diffraction. Notably, when incident waves strike a corner, diffracted waves emanate from the…
An inverse coefficient problem for a semilinear wave equation by the first order linearization
Yuxiang He, Shuai Lu
This paper investigates recovery of an unknown coefficient in a semilinear wave equation defined on a bounded, open, and strictly convex domain in \(\mathbb{R}^{1+n}\) with \(n \ge…
Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds
Xi Chen, Shuai Lu, Ruochong Zhang
We study the recovery of a smooth nonlinearity in semilinear wave equations on globally hyperbolic Lorentzian manifolds. Our approach combines higher-order linearization with disto…
Functional analysis and partial differential equations in spectral Barron spaces
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations…
A highly scalable numerical framework for reservoir simulation on UG4 platform
Shuai Lu
The modeling and simulation of multiphase fluid flow receive significant attention in reservoir engineering. Many time discretization schemes for multiphase flow equations are eith…
Stability for an inverse flux and an inverse boundary coefficient problems
Mourad Choulli, Shuai Lu, Hiroshi Takase
We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Further…
Interpolation and inverse problems in spectral Barron spaces
Shuai Lu, Peter Mathé
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal a…
Stable inversion of potential in nonlinear wave equations with cubic nonlinearity
Xi Chen, Shuai Lu, Ruochong Zhang
This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower o…
Function and derivative approximation by shallow neural networks
Yuanyuan Li, Shuai Lu
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown…
Forward and backward problems for coupled subdiffusion systems
Dian Feng, Yikan Liu, Shuai Lu
In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the fo…
A linearised inverse conductivity problem for the Maxwell system at a high frequency
Victor Isakov, Shuai Lu, Boxi Xu
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds…