Zobrazeno 1 - 10
of 159
pro vyhledávání: '"Zhong, Yimin"'
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to approximate functions with complex features with both accuracy and efficiency in terms of degrees of freedom and computation cost. The main idea is
Externí odkaz:
http://arxiv.org/abs/2407.00765
Autor:
Wang, Yiran, Zhong, Yimin
The limited angle Radon transform is notoriously difficult to invert due to the ill-posedness. In this work, we give a mathematical explanation that the data-driven approach based on deep neural networks can reconstruct more information in a stable w
Externí odkaz:
http://arxiv.org/abs/2403.11350
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provides a systematic error analysis for IBIMs on uniform Cartesian grids fo
Externí odkaz:
http://arxiv.org/abs/2312.07722
In this work, a comprehensive numerical study involving analysis and experiments shows why a two-layer neural network has difficulties handling high frequencies in approximation and learning when machine precision and computation cost are important f
Externí odkaz:
http://arxiv.org/abs/2306.17301
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear radiative t
Externí odkaz:
http://arxiv.org/abs/2210.17024
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with improved accuracy for a boundary integral formulation of the linearize
Externí odkaz:
http://arxiv.org/abs/2210.03699
Autor:
Zhao, Hongkai, Zhong, Yimin
Linear evolution PDE $\partial_t u(x,t) = -\mathcal{L} u$, where $\mathcal{L}$ is a strongly elliptic operator independent of time, is studied as an example to show if one can superpose snapshots of a single (or a finite number of) solution(s) to con
Externí odkaz:
http://arxiv.org/abs/2206.05336
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the underlying
Externí odkaz:
http://arxiv.org/abs/2204.04602
We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We also repo
Externí odkaz:
http://arxiv.org/abs/2202.11888
Autor:
Stefanov, Plamen, Zhong, Yimin
This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If scattering
Externí odkaz:
http://arxiv.org/abs/2104.06566