32 citations · 86 across the 14 of their papers we have counts for
14 papers
Level-set physics-informed neural networks for domain inverse problems of gravimetry
Jingnan Yao, Wenbin Li, Jianliang Qian
We propose level-set physics-informed neural networks (PINNs) for domain inverse problems of gravimetry. The domain inverse problem establishes a correctness class for ill-posed in…
Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing
Yuxiao Wei, Jin Cheng, Robert Burridge +1
We propose a novel Hadamard integrator for the self-adjoint time-dependent wave equation in an inhomogeneous medium. First, we create a new asymptotic series based on the Gelfand-S…
Operator Splitting/Finite Element Methods for the Minkowski Problem
Hao Liu, Shingyu Leung, Jianliang Qian
The classical Minkowski problem for convex bodies has deeply influenced the development of differential geometry. During the past several decades, abundant mathematical theories ha…
A Fast Butterfly-compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources
Yang Liu, Jian Song, Robert Burridge +1
We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media.…
An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation
Hao Liu, Shingyu Leung, Jianliang Qian
We develop an efficient operator-splitting method for the eigenvalue problem of the Monge-Ampère operator in the Aleksandrov sense. The backbone of our method relies on a convergen…
Learning Rays via Deep Neural Network in a Ray-based IPDG Method for High-Frequency Helmholtz Equations in Inhomogeneous Media
Tak Shing Au Yeung, Ka Chun Cheung, Eric T. Chung +2
We develop a deep learning approach to extract ray directions at discrete locations by analyzing highly oscillatory wave fields. A deep neural network is trained on a set of local…
On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator
Roland Glowinski, Shingyu Leung, Hao Liu +1
In this article, we report the results we obtained when investigating the numerical solution of some nonlinear eigenvalue problems for the Monge-Ampère operator $v\rightarrow \det…
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…
A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media
Eric T. Chung, Chi Yeung Lam, Jianliang Qian
The numerical approximation of high-frequency wave propagation in inhomogeneous media is a challenging problem. In particular, computing high-frequency solutions by direct simulati…
Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians
Jianliang Qian, Hung V. Tran, Yifeng Yu
This paper is the first attempt to systematically study properties of the effective Hamiltonian arising in the periodic homogenization of some coercive but nonconvex…
Perfectly-matched-layer boundary integral equation method for wave scattering in a layered medium
Wangtao Lu, Ya Yan Lu, Jianliang Qian
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or inte…
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…
Iterative Algorithms for Ptychographic Phase Retrieval
C. Yang, J. Qian, A. Schirotzek +2
Ptychography promises diffraction limited resolution without the need for high resolution lenses. To achieve high resolution one has to solve the phase problem for many partially o…
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…