Research interests

Numerical methods, applied analysis, and mathematical modeling for

1. kinetic theory;
2. gradient flows, optimal transport;
3. conservation laws, fluid dynamics;
4. inverse problems;

with applications in physics, engineering, biology and data science.

Publications

Preprints:

To blow-up or not to blow-up for a granular kinetic equation (with J. Carrillo, R. Shu and W. Xu), submitted. arXiv

Radiative transport in a periodic structure with band crossings (with K. Qi and A. Watson), submitted. arXiv

Deep JKO: Time-implicit particle methods for general nonlinear gradient flows (with W. Lee and W. Li), submitted. arXiv

On the kinetic description of the objective molecular dynamics (with R. D. James and K. Qi), submitted. arXiv

Uniform error estimate of an asymptotic preserving scheme for the Levy-Fokker-Planck equation (with W. Sun), submitted. arXiv

Refereed journal or conference publications:

Differential-equation constrained optimization with stochasticity (with Q. Li and Y. Yang), SIAM/ASA Journal on Uncertainty Quantification, accepted. arXiv

Suppressing instability in a Vlasov-Poisson system by an external electric field through constrained optimization (with L. Einkemmer, Q. Li and Y. Yang), J. Comput. Phys. 2024. journal arXiv

Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances (with J. Carrillo and C. Wei), SIAM J. Numer. Anal., accepted. arXiv

Monte Carlo gradient in optimization constrained by radiative transport equation (with Q. Li and Y. Yang), SIAM J. Numer. Anal., accpeted. journal arXiv

Transfer learning enhanced DeepONet for long-time prediction of evolution equations (with Y. Lu and W. Xu), The 37th AAAI conference on Artificial Intelligence, 2023. arXiv Code

Solving multiscale steady radiative transfer equation using neural networks with uniform stability (with Y. Lu and W. Xu), Research in Mathematical Sciences 9, 2022. journal arXiv

Hessian informed mirror descent (with M. Yan), J. Sci. Comput. 92, 2022. journal arXiv

Bayesian instability of optical imaging: ill conditioning of inverse linear and nonlinear radiative transfer equation in the fluid fegime (with Q. Li and K. Newton), Computation, 2022. journal

An asymptotic preserving scheme for L'evy-Fokker-Planck equation with fractional diffusion limit (with W. Xu), Comm. Math. Sci. 21, No. 1, 1–21, 2023. arXiv journal

A proximal-gradient algorithm for crystal surface evolution (with K. Craig, J.-G. Liu, J. Lu, J. Marzuola), Numerische Mathematik 152, 631–662, 2022. journal arXiv

Self-similarity in particle accumulation on the advancing meniscus (with Y. Chen, R. Luo and S. Lee), J. Fluid Mech., 2021. journal

Variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system (with J. A. Carrillo, W. Xu and M. Yan), Multiscale Model. Simul., 19(1), 478-–505, 2021. arXiv journal

Primal dual methods for Wasserstein gradient flows (with J. A. Carrillo, K. Craig and C. Wei), Foundations of Computational Mathematics, 2021. arXiv journal

A particle method for the homogeneous Landau equation (with J. Carrillo, J. Hu and J. Wu), J. Comput. Phys. 7, 100066, 2020. arXiv journal

Fisher information regularization schemes for Wasserstein gradient flows (with W. Li and J. Lu), J. Comput. Phys. 416, 109449, 2020. arXiv journal

Towards understanding the boundary propagation speeds in tumor growth models (with J.-G. Liu, M. Tang and Z. Zhou), SIAM. J. Appl. Math., 2021. journal arXiv

Accurate front capturing asymptotic preserving method for nonlinear grey radiative transport equation (with M. Tang and X. Zhang), SIAM J. Sci. Comput, accepted, 2021. arXiv

An asymptotic-preserving scheme for kinetic equation with anisotropic scattering: heavy tail equilibrium and degenerate collision frequency (with B. Yan), SIAM. J. Sci. Comput. 41(1), A422-–A451, 2019. journal

Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics (with J.-G. Liu, M. Tang and Z. Zhou), DCDS-B 24(7): 3011–3035, 2019. journal

A new numerical approach to inverse transport equation with error analysis (with Q. Li and R. Shu), SIAM. J. Numer. Anal 56, No.6, 3358–3385, 2018. arXi journal

Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit (with K. Chen and Q. Li), SIAM J. Appl. Math. 78, No.5, 2626–2647, 2018. arXiv journal

Crime modeling with truncated Levy flights for residential burglary models (with C. Pan, B. Li, C. Wang, Y. Zhang, N. Geldner, A. L. Bertozzi), Math. Models Methods Appl. Sci. 28, No.9, 1857–1880, 2018. arXiv journal

Modeling and simulations of particle-laden flow with surface tension (with A. Mavromoustaki, J. Wong and A. L. Bertozzi), Nonlinearity 31, No.7, 3151–3173, 2018. journal

An accurate front capturing scheme for tumor growth models with a free boundary limit (with J.-G. Liu, M. Tang and Z. Zhou), J. Comput. Phys. 364, 73–94, 2018. arXiv journal

Stability of stationary inverse transport equation in diffusion scaling (with. K. Chen and Q. Li), Inverse Problems. 34, No. 2, 2018. arXiv journal

Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations (with J.-G. Liu and Z. Zhou), Math. Comp. 87, 1165–1189, 2018. journal

Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar hyperbolic conservation laws (with F. Coquel, S. Jin and J.-G. Liu), Math. Comp. 87, 1083–1126, 2018. journal

Uniform regularity for linear kinetic equations with random input based on hypocoercivity (with Q. Li), SIAM J. Uncer. Quan., 5 (1), 1193–1219, 2017. arXiv journal

Implicit asymptotic preserving method for linear transport equation (with Q. Li), Comm. Comput. Phys. 22, issue 1, 157–181, 2017. journal

Efficient numerical schemes for multiscale crowd dynamics with emotional contagion (with M. Short and A. L. Bertozzi), Math. Models Methods Appl. Sci. 27, no. 1, 205–230, 2017. journal

An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit (with B. Yan), J. Comput. Phys. 312, 157–174, 2016. journal

The ADI methods for two-dimensional nonlinear multidelay parabolic equations (with Q. Zhang, C. Zhang), J. Comp. Appl. Math. 306, 217–230, 2016. journal

An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach (with J. Hu and S. Jin), Kinetic and Related Models 8, 707–723, 2015. journal

Rarefaction-singular shock solution for conserved volume gravity driven particle-laden thin film (with A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta and K. Huang), Phys. Fluids 27, 033301, 2015. journal

An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit (with J. Hu), J. Comput. Phys. 281, 806–821, 2015. journal

Contagion shocks in one dimension (with A. L. Bertozzi, J. Rosado, and M. Short), J. Stat. Phys. 3, Vol. 158, 647–664, 2015. journal

Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate (with F. Coquel, S. Jin, and J. G. Liu), Arch. Rat. Mech. Anal. 214, 1051–1084, 2014. journal

Shock solutions for high concentration particle laden thin films (with A. L. Bertozzi), SIAM J. Appl. Math., 74(2), 322–344, 2014. journal

Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime (with S. Jin), SIAM J. Sci. Comp. 35, B799–B819, 2013. journal

A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations (with S. Jin and J. G. Liu), Math. Comp. 82, 749–779, 2013. link

An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime (with S. Jin), Acta Mathematica Scientia 31, 2219–2232, 2011. Special issue in honor of Peter Lax’s 85th birthday. link

Others:

Multiscale physical problems: asymptotics and asmptotic-preserving Schemes (with S. Jin, L. Li and Z. Zhou), Panoramas et Syntheses, 2022.