11 citations · 56 across the 26 of their papers we have counts for
14 papers · 1 filter
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…
A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems
Sijing Li, Cheng Zhang, Zhiwen Zhang +1
In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to…
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 data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction
Sijing Li, Zhiwen Zhang, Hongkai Zhao
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential…
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…
A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez +1
We propose a hybrid approach to solve the high-frequency Helmholtz equation with point source terms in smooth heterogeneous media. The method is based on the ray-based finite eleme…
Learning Dominant Wave Directions For Plane Wave Methods For High-Frequency Helmholtz Equations
Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez +1
We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics…
Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds
Meng Wang, Shingyu Leung, Hongkai Zhao
We propose a new and simple discretization, named the Modified Virtual Grid Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB) operator on manifolds sample…
Fast alternating bi-directional preconditioner for the 2D high-frequency Lippmann-Schwinger equation
Leonardo Zepeda-Núñez, Hongkai Zhao
This paper presents a fast iterative solver for Lippmann-Schwinger equation for high-frequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solv…
Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap
Rongjie Lai, Hongkai Zhao
In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation. First, point clouds sampled from manifolds originally embed…
A New Numerical Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed
Jianliang Qian, Plamen Stefanov, Gunther Uhlmann +1
We present a new algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature…