What Can One Expect When Solving PDEs Using Shallow Neural Networks? [with Y. He, H. Zhao, Y. Liang], submitted. [pdf]

Forward and inverse problems of a semilinear transport equation [with K. Ren], submitted. [pdf]

Fourier multi-component and multi-layer neural networks: unlocking high-frequency potential [with S. Zhang, H. Zhao, H. Zhou], submitted. [pdf][code]

Robustness of data-driven approaches in limited angle tomography [with  Y. Wang], SIAM Journal on Imaging Sciences 18 (1), 345-358 [pdf][code]

Structured and balanced multi-component and multi-layer neural networks [with S. Zhang, H. Zhao, H. Zhou], SIAM Journal on Scientific Computing 47(5), C1059-C1090. [pdf][code]

Error analysis for implicit boundary integral method [with K. Ren, R. Tsai, O. Runborg], BIT Numerical Mathematics 65 (1), 8 [pdf][code]

Why shallow networks struggle with approximating and learning high frequency [with S. Zhang, H. Zhao, H. Zhou], Information and Inference: A Journal of the IMA 14 (3). [pdf]

Transport models for wave propagation in scattering media with nonlinear absorption [with J. Kraisler, W. Li,  K. Ren,  J. Schotland], SIAM J. Applied Math 83.4 (2023), 1677 - 1695. [pdf]

Corrected trapezoidal rule-IBIM for linearized Poisson-Boltzmann equation [with F. Izzo, O. Runborg, R. Tsai], submitted. [pdf][code]

How much can one learn from a single solution of a PDE? [with H. Zhao], accepted by Pure and Applied Functional Analysis, 2022. [pdf][code] 

Inverse source problem in ultrasound modulated Maxwell equations  [with W. Li, J. Schotland, Y. Yang], SIAM J. Applied Math. 83.2 (2023), 418-435. [pdf][code]

How much can one learn a partial differential equation from its solution?  [with Y. He and H. Zhao], Foundations of Computational Mathematics (2023), 1-47. [pdf]

Inverse boundary problem for the two-photon transport equation [with P. Stefanov], SIAM J. Math Anal 54.3 (2022): 2753-2767. [pdf]

Acousto-electric Inverse Source Problems [with W. Li, J. Schotland, Y. Yang], SIAM J. Imaging Sci., 14 (4), 1601-1616, 2021. [pdf] [code]

A hybrid reconstruction method for optical tomography [with H. Zhao], preprint.

Unique determination of absorption coefficients in a semilinear transport equation [with K. Ren], SIAM J.  Math Anal.,  53 (5), 5158–5184, 2021 [pdf]

Quantitative PAT with simplified PN approximation [with H. Zhao],  Inverse Problems, 37.5  (2021), 055009. [pdf] [code]

Separability of the kernel function in an integral formulation for anisotropic radiative transfer equation [with H. Zhao and K. Ren], SIAM J.  Math Anal., 53 (5), 5613-5645, 2021. [pdf]

Reconstruction of acoustic and optical properties in PAT/TAT with data from multiple illuminations [with K. Ren],  preprint.

A fast numerical algorithm for time-dependent radiative transport [with H. Zhao], CSIAM Trans. Appl. Math., 1 (2020), pp. 346-364. [pdf][code]

A fast algorithm for radiative transport in isotropic media [with K. Ren and R. Zhang],  Journal of Computational Physics,  399 (2019), 108958. [pdf][code]

Imaging point sources in heterogeneous media [with K. Ren],  Inverse Problems, 35(12), 125003, 2019. [pdf][code]

An inverse transport problem in the fluorescence ultrasound modulated optical tomography [with W. Li and Y. Yang], Inverse Problems, 36.2 (2020), 025011. [pdf][code]

Instability of the inverse problem for the stationary radiative transport equation [with H. Zhao],  SIAM J. Math Anal., 51(5), 3750-3768, 2019. [pdf]

Intrinsic complexity and scaling laws: from random fields to random vectors [with J. Bryson and H. Zhao], Multiscale Model. Simul., 17(1), 460-481, 2019. [pdf]

A hybrid inverse problem in the fluorescence ultrasound modulated optical tomography in diffusive regime [with W. Li and Y. Yang], SIAM J. Appl. Math., 79(1), 356-376, 2019. [pdf][code]

A hybrid adaptive phase space method for reflection traveltime tomography [with H. Zhao], SIAM J. Imaging Sci., 12(1), 28-53, 2019. [pdf][code]

An implicit boundary integral method for computing electric potential of macromolecules in solvent [with K. Ren and R. Tsai], Journal of Computational Physics 359 (2018): 199-215. [pdf][code]

Inverse transport problems in quantitative PAT for molecular imaging [with K. Ren and R. Zhang], Inverse Problems, 31, 125012, 2015. [pdf]