19 citations · 72 across the 23 of their papers we have counts for
10 papers · 1 filter
A Multi-Level Machine Learning Framework for Inverse Scattering Problems with Multi-Frequency Data
Yi Liu, Yanzhao Cao, Junshan Lin +1
In this work, we propose a multi-level machine learning framework for solving inverse scattering problems with multi-frequency data. The multi-level neural network is built along t…
Corrected Trapezoidal Rule-IBIM for linearized Poisson-Boltzmann equation
Federico Izzo, Yimin Zhong, Olof Runborg +1
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…
How much can one learn from a single solution of a PDE?
Hongkai Zhao, Yimin Zhong
Linear evolution PDE , where is a strongly elliptic operator independent of time, is studied as an example to show if one can supe…
How much can one learn a partial differential equation from its solution?
Yuchen He, Hongkai Zhao, Yimin Zhong
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…
Quantitative PAT with simplified approximation
Hongkai Zhao, Yimin Zhong
The photoacoustic tomography (PAT) is a hybrid modality that combines the optics and acoustics to obtain high resolution and high contrast imaging of heterogeneous media. In this w…
A fast algorithm for time-dependent radiative transport equation based on integral formulation
Hongkai Zhao, Yimin Zhong
In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies th…
Separability of the kernel function in an integral formulation for anisotropic radiative transfer equation
Kui Ren, Hongkai Zhao, Yimin Zhong
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The inte…
A hybrid adaptive phase space method for reflection traveltime tomography
Hongkai Zhao, Yimin Zhong
We present a hybrid imaging method for a challenging travel time tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to re…
An implicit boundary integral method for computing electric potential of macromolecules in solvent
Yimin Zhong, Kui Ren, Richard Tsai
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics o…
A fast algorithm for radiative transport in isotropic media
Kui Ren, Rongting Zhang, Yimin Zhong
We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we deriv…