19 citations · 72 across the 23 of their papers we have counts for
24 papers
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…
Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential
Shijun Zhang, Hongkai Zhao, Yimin Zhong +1
The architecture of a neural network and the choice of its activation function are both fundamental to its performance. Equally important is ensuring that these two elements are we…
Structured and Balanced Multi-Component and Multi-Layer Neural Networks
Shijun Zhang, Hongkai Zhao, Yimin Zhong +1
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in te…
Why Shallow Networks Struggle to Approximate and Learn High Frequencies
Shijun Zhang, Hongkai Zhao, Yimin Zhong +1
In this work, we present a comprehensive study combining mathematical and computational analysis to explain why a two-layer neural network struggles to handle high frequencies in b…
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…
Transport models for wave propagation in scattering media with nonlinear absorption
Joseph Kraisler, Wei Li, Kui Ren +2
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 Wign…
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…
Inverse Source Problem for Acoustically-Modulated Electromagnetic Waves
Wei Li, John C. Schotland, Yang Yang +1
We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the curren…
Inverse Boundary Problem for the Two Photon Absorption Transport Equation
Plamen Stefanov, Yimin Zhong
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…
Acousto-electric Inverse Source Problem
Wei Li, John C. Schotland, Yang Yang +1
We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show th…
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…
Unique determination of absorption coefficients in a semilinear transport equation
Kui Ren, Yimin Zhong
Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorpt…
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…
Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements
Wei Li, Yang Yang, Yimin Zhong
We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the unique…
Imaging point sources in heterogeneous environments
Kui Ren, Yimin Zhong
Imaging point sources in heterogeneous environments from boundary or far-field measurements has been extensively studied in the past. In most existing results, the environment, rep…
Instability of an inverse problem for the stationary radiative transport near the diffusion limit
Hongkai Zhao, Yimin Zhong
In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean…
Intrinsic Complexity And Scaling Laws: From Random Fields to Random Vectors
Jennifer Bryson, Hongkai Zhao, Yimin Zhong
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a…
A hybrid inverse problem in the fluorescence ultrasound modulated optical tomography in the diffusive regime
Wei Li, Yang Yang, Yimin Zhong
We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the absorption coefficient of the flu…
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…
Inverse transport problems in quantitative PAT for molecular imaging
Kui Ren, Rongting Zhang, Yimin Zhong
Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imagin…