Journal ArticleFoundations of Computational Mathematics · October 1, 2024
In this work, we study the problem of learning a partial differential equation (PDE) from its solution data. PDEs of various types are used to illustrate how much the solution data can reveal the PDE operator depending on the underlying operator and initia ...
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Journal ArticleStatistics and Computing · August 1, 2023
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 accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale B ...
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ConferenceProceedings of Machine Learning Research · January 1, 2023
This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expr ...
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Journal ArticleInverse Problems · May 1, 2021
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 work, our objective is to study the inverse problem in the quantitative step ...
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ConferenceProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition · January 1, 2021
In this work, a robust and efficient dual iterative refinement (DIR) method is proposed for dense correspondence between two nearly isometric shapes. The key idea is to use dual information, such as spatial and spectral, or local and global features, in a ...
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Journal ArticleProceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition · 2020Full textCite
Journal ArticleSIAM Journal on Imaging Sciences · January 1, 2019
We present a hybrid imaging method for a challenging traveltime tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to recover both the medium and the boundary of the scatterers from the scattering ...
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Journal ArticleMultiscale Modeling and Simulation · January 1, 2019
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 random field in terms of its second order statistics, e.g., the covariance f ...
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Journal ArticleCommunications on Pure and Applied Mathematics · November 2018
AbstractThe minimum number of terms that are needed in a separable approximation for a Green's function reveals the intrinsic complexity of the solution space of the underlying differential equation. It also has implication ...
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Journal ArticleGEOPHYSICS · March 2012
In the geometrical-optics approximation for the Helmholtz equation with a point source, traveltimes and amplitudes have upwind singularities at the point source. Hence, both first-order and higher-order finite-difference solvers exhibit formally at ...
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Journal ArticleCommunications in Computational Physics · August 2011
AbstractIn this paper, we numerically investigate the effects of surfactant on drop-drop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in (Xu et al., J. Comput. Phys., 21 ...
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Journal ArticleThe Journal of Chemical Physics · April 14, 2009
The Poisson–Boltzmann theory has become widely accepted in modeling electrostatic solvation interactions in biomolecular calculations. However the standard practice of atomic point charges in molecular mechanics force fields introduces singularity ...
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Journal ArticleThe Journal of the Acoustical Society of America · January 1, 2009
A direct imaging algorithm for point and extended targets is presented. The algorithm is based on a physical factorization of the response matrix of a transducer array. The factorization is used to transform a passive target problem to an active so ...
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Journal ArticleMathematics of Computation · May 21, 2004
In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with al ...
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Journal ArticleThe Journal of the Acoustical Society of America · January 1, 2002
The phenomenon of super-resolution in time-reversal acoustics is analyzed theoretically and with numerical simulations. A signal that is recorded and then retransmitted by an array of transducers, propagates back though the medium, and refocuses ap ...
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