List of Publications
Submitted:
1. Frozen Gaussian approximations for the fractional Schr\"odinger equation (with Lihui Chai and Hengzhun Chen); [arXiv:2403.18287]
2. Error estimates of physics-informed neural networks for approximating Boltzmann equation (with Elie Abdo, Lihui Chai and Ruimeng Hu); [arXiv:2407.08383]
Accepted:
1. Unfitted spectral element method for interfacial models (with Nicolas Gonzalez and Hailong Guo), Commun. Comput. Phys.; [arXiv:2309.17027]
2. Integrating Sequential Hypothesis Testing into Adversarial Games: A Sun Zi-Inspired Framework (with Haosheng Zhou, Daniel Ralston and Ruimeng Hu), accepted for the 64th IEEE Conference on Decision and Control (CDC); [arXiv:2502.13462]
Published:
[70]. Informed Normalized Gradient Flow Method for Parameterized Schrödinger Operators: A Case Study on Photonic Graphene (with Hailong Guo, Emmanuel Lorin and Charlotte Noxon); J. Sci. Comput., 103:76, 2025; [journal]
[69].Semi-classical limit of the Dirac equation in curved space and applications to strained and photonic graphene (with Fran\c{c}ois Fillion-Gourdeau, Emmanuel Lorin and Steve MacLean); J. Phys. A: Mathematical and Theoretical, 58, 115302, 2025; [journal]
[68]. Multi-Agent Relative Investment Games in a Jump Diffusion Market with Deep Reinforcement Learning Algorithm (with Liwei Lu, Ruimeng Hu and Yi Zhu), SIAM Journal on Financial Mathematics, 16, 707-746, 2025; [arXiv] [journal]
[67]. Temporal difference learning for high-dimensional PIDEs with jumps (with Liwei Lu, Hailong Guo and Yi Zhu), SIAM J. Sci. Comput., 46, C349--C368, 2024; [arXiv] [journal]
[66]. Computational wavefunction dynamics in photonic graphene with symmetry breaking (with Emmanuel Lorin), Applied Numerical Mathematics, 199, 85--104, 2024; [ResearchGate] [journal]
[65]. Quasi-optimal domain decomposition method for neural network-based computation of the time-dependent Schr\"odinger equation (with Emmanuel Lorin), Comput. Phys. Comm., 299, 109129, 2024; [journal]
[64]. Frozen Gaussian approximation for the Dirac equation in curved space with application to strained graphene (with Lihui Chai and Emmanuel Lorin), Commun. Comput. Phys., 34, 18--37, 2023; [journal]
[63]. Seismic tomography with random batch gradient reconstruction (with Yixiao Hu, Lihui Chai and Zhongyi Huang), SIAM. J. Sci. Comput., 45, B314--B336, 2023; [arXiv] [journal]
[62]. Schwarz waveform relaxation physics-informed neural networks for solving advection-diffusion-reaction equations (with Emmanuel Lorin), J. Comput. Phys., 473, 111657, 2023; [arXiv] [journal]
[61]. Time-dependent Dirac equation with Physics-Informed Neural Networks: Computation and properties (with Emmanuel Lorin), Comput. Phys. Comm., 280, 108474, 2022;[arXiv] [journal]
[60]. Convergence analysis on seismic tomography for inverse problems of acoustic wave propagation (with Haoyu Wang, Lihui Chai and Zhongyi Huang), Commun. Math. Sci., 20, 1551--1565, 2022; [journal]
[59]. Deep neural networks for creating reliable PmP database with a case study in Southern California (with Wen Ding, Tianjue Li, Kui Ren and Ping Tong), JGR Solid Earth, 127, e2021JB023830, 2022; [arXiv] [journal]
[58]. Deep unfitted Nitsche method for elliptic interface problems (with Hailong Guo), Commun. Comput. Phys., 31, 1162--1179, 2022; [arXiv] [journal]
[57]. Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging (with Ziju Shen, Yufei Wang, Dufan Wu and Bin Dong), Inverse Problems and Imaging, 16, 179--195, 2022; [arXiv] [journal]
[56]. Unfitted Nitsche's method for computing band structures of phononic crystals with periodic inclusions (with Hailong Guo and Yi Zhu), Computer Methods in Applied Mechanics and Engineering, 380, 113743, 2021; [arXiv] [journal]
[55]. Unfitted Nitsche's method for computing wave modes in topological materials (with Hailong Guo and Yi Zhu), J. Sci. Comput., 88, 24, 2021; [arXiv] [journal]
[54]. Semi-classical limit for the varying-mass Schr\"odinger equation with random inhomogeneities (with Shi Chen and Qin Li), J. Comput. Phys., 438, 110365, 2021; [arXiv] [journal]
[53]. On the Convergence of Frozen Gaussian Approximation for linear non-strictly hyperbolic systems (with Lihui Chai, James C. Hateley and Emmanuel Lorin), Commun. Math. Sci., 19, 585--606, 2021; [ResearchGate] [journal]
[52]. Deep learning seismic substructure detection using the frozen Gaussian approximation (with James C. Hateley, Jay Roberts and Kyle Mylonakis), J. Comput. Phys., 409, 109313, 2020; [arXiv] [journal]
[51]. Frozen Gaussian approximation for the Dirac equation in the semiclassical regime (with Lihui Chai and Emmanuel Lorin), SIAM J. Numer. Anal., 57, 2383--2412, 2019; [ResearchGate] [journal]
[50]. Frozen Gaussian approximation for 3-D elastic wave equation and seismic tomography (with James C. Hateley, Lihui Chai and Ping Tong), Geophys. J. Int., 216, 1394--1412, 2019; [arXiv] [doi] [journal]
[49]. Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene (with Hailong Guo and Yi Zhu), J. Comput. Phys., 379, 403--420, 2019; [arXiv] [doi] [journal]
[48]. Frozen Gaussian approximation for high frequency wave propagation in periodic media (with Ricardo Delgadillo and Jianfeng Lu), Asymptot. Anal., 110, 113--135, 2018; [arXiv] [journal]
[47]. Diffusion limit of the Wigner-Landau-Lifshitz-Gilbert system in ferromagnetic materials (with Lihui Chai and Carlos J. Garcia-Cervera), Commun. Math. Sci., 16, 1157--1167, 2018; [journal]
[46]. Superconvergence analysis of partially penalized immersed finite element methods (with Hailong Guo and Zhimin Zhang), IMA J. Numer. Anal., 38, 2123--2144, 2018; [arXiv] [journal]
[45]. Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schr\"odinger equation in the semiclassical regime (with Ricardo Delgadillo and Jiwei Zhang, ), J. Sci. Comput., 75, 1701--1720, 2018; [journal]
[44]. Frozen Gaussian approximation for 3-D seismic tomography (with Lihui Chai and Ping Tong), Inverse Problems, 34, 055004, 2018; [journal]
[43]. Gradient recovery for elliptic interface problem: I. body-fitted mesh (with Hailong Guo), Commun. Comput. Phys., 23, 1488--1511, 2018; [arXiv] [journal]
[42]. Semiclassical limit of the Schr\"odinger-Poisson-Landau-Lifshitz-Gilbert system (with Lihui Chai and Carlos J. Garcia-Cervera), Arch. Rational Mech. Anal., 227, 897--928, 2018; [journal]
[41]. Gradient recovery for elliptic interface problem: III. Nitsche's method (with Hailong Guo), J. Comput. Phys., 356, 46--63, 2018; [arXiv] [journal]
[40]. Gradient recovery for elliptic interface problem: II. immersed finite element method (with Hailong Guo), J. Comput. Phys., 338, 606--619, 2017; [arXiv] [journal]
[39]. Polynomial preserving recovery for high frequency wave propagation (with Hailong Guo), J. Sci. Comput., 71, 594--614, 2017; [journal]
[38]. Frozen Gaussian approximation for 3-D seismic wave propagation (with Lihui Chai and Ping Tong), Geophys. J. Int., 208, 59--74, 2017; [journal]
[37]. Frozen Gaussian approximation-based two-level methods for multi-frequency Schr\"odinger equation (with Emmanuel Lorin), Comput. Phys. Comm., 207, 145--159, 2016; [journal]
[36]. Gauge-invariant frozen Gaussian approximation method for the Schr\"odinger equation with periodic potentials (with Ricardo Delgadillo and Jianfeng Lu), SIAM J. Sci. Comput., 38, A2440--A2463, 2016; [arXiv] [journal]
[35]. Frozen Gaussian approximation based domain decomposition methods for the linear Schr\"odinger equation beyond the semi-classical regime (with Emmanuel Lorin and Xavier Antonie), J. Comput. Phys., 315, 221--237, 2016; [journal]
[34]. Acoustic wave-equation-based earthquake location (with Ping Tong, Dinghui Yang, Qinya Liu and Jerry Harris), Geophys. J. Int., 205, 464--478, 2016; [journal]
[33]. An augmented Keller-Segel model for E. coli chemotaxis in fast-varying environments (with Tong Li and Min Tang), Commun. Math. Sci., 14, 883--891, 2016; [journal]
[32]. A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion (with Jinglai Li and Guang Lin), J. Comput. Phys., 296, 58--71, 2015; [journal]
[31]. Mean-field dynamics of spin magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motion (with Jingrun Chen and Carlos J. Garcia-Cervera), IEEE Transactions on Magnetics, 51, 1400906, 2015; [journal]
[30]. A mean-field model for spin dynamics in multilayered ferromagnetic media (with Jingrun Chen and Carlos J. Garcia-Cervera and X. Yang), (SIAM) Multiscale Model. Simul., 13, 551--570, 2015; [journal]
[29]. Wave-equation based traveltime seismic tomography: II. Application to the 1992 Landers earthquake (with Ping Tong, Dapeng Zhao, Dinghui Yang, Jingrun Chen and Qinya Liu), Solid Earth, 5, 1169--1188, 2014; [journal]
[28]. Wave-equation based traveltime seismic tomography: I. Method (with Ping Tong, Dapeng Zhao, Dinghui Yang, Jingrun Chen and Qinya Liu), Solid Earth, 5, 1151--1168, 2014; [journal]
[27]. A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and its hyperbolic and parabolic limits (with Guangwei Si and Min Tang), (SIAM) Multiscale Model. Simul., 12, 907--926, 2014; [arXiv] [journal]
[26]. Computation of the Schr\"odinger equation in the semiclassical regime on unbounded domain (with Jiwei Zhang), SIAM J. Numer. Anal., 52, 808--831, 2014; [journal]
[25]. Exponential Runge-Kutta methods for the multispecies Boltzmann equation (with Qin Li), Commun. Comput. Phys., 15, 996--1011, 2014; [journal]
[24]. Seismic modeling using the frozen Gaussian approximation (Jianfeng Lu and Sergey Fomel), SEG Technical Program Expanded Abstracts 2013, 4677--4682; [arXiv] [conference]
[23]. Asymptotic analysis of the quantum dynamics in crystals: The Bloch-Wigner transform, Bloch dynamics and Berry phase (with Weinan E and Jianfeng Lu), Acta Math. Appl. Sin. Engl. Ser., 29, 465--476, 2013; [journal]
[22]. Eulerian Gaussian beam method for high frequency wave propagation in the reduced momentum space (with Hao Wu), Wave Motion, 50, 1036--1049, 2013; [journal]
[21]. Eulerian Gaussian beam method for high frequency wave propagation in heterogeneous media with discontinuities in one direction (with Dongming Wei), Commun. Math. Sci., 10, 1287--1299, 2012; [journal]
[20]. Tailored finite cell method for computing Helmholtz equation in layered heterogeneous medium (with Zhongyi Huang), J. Comput. Math., 30, 381--391, 2012; [journal]
[19]. Frozen Gaussian approximation for general linear strictly hyperbolic systems: Formulation and Eulerian methods (with Jianfeng Lu), (SIAM) Multiscale Model. Simul., 10, 451--472, 2012; [journal]
[18]. Convergence of frozen Gaussian approximation for high frequency wave propagation (with Jianfeng Lu), Comm. Pure Appl. Math., 65, 759--789, 2012; [arXiv] [journal]
[17]. Tailored finite point method for first order wave equation (with Zhongyi Huang), J. Sci. Comput., 49, 351--366, 2011; [journal]
[16]. A hybrid phase-flow method for solving the Liouville equation in bounded domain (with Hao Wu), SIAM J. Numer. Anal., 49, 733--754, 2011; [journal]
[15]. Frozen Gaussian approximation for high frequency wave propagation (with Jianfeng Lu), Commun. Math. Sci., 9, 663--683, 2011; [arXiv] [journal]
[14]. Effective Maxwell equations from time-dependent density functional theory (with Weinan E and Jianfeng Lu), Acta Math. Sin., 27, 339--368, 2011; [journal]
[13]. Semi-Eulerian and high order Gaussian beam methods for the Schr\"odinger equation in the semiclassical regime (with Shi Jin and Hao Wu), Commun. Comput. Phys., 9, 668--687, 2011; [journal]
[12]. Level set method for the semiclassical limit of the Schr\"odinger equation with discontinuous potential (with Dongming Wei, Shi Jin and Richard Tsai), J. Comput. Phys., 229, 7440--7455, 2010; [journal]
[11]. Bloch decomposition-based Gaussian beam method for the Schr\"odinger equation with periodic potentials (with Shi Jin, Hao Wu and Zhongyi Huang), J. Comput. Phys., 229, 4869--4883, 2010; [journal]
[10]. A numerical study of the Gaussian beam methods for one-dimensional Schr\"odinger-Poisson equations (with Shi Jin and Hao Wu), J. Comput. Math., 28, 261--272, 2010; [journal]
[9]. Gaussian beam methods for the Schr\"odinger equation in the semi-classical regime: Lagrangian and Eulerian formulations (with Shi Jin and Hao Wu), Commun. Math. Sci., 6, 995--1020, 2008; [journal]
[8] The Vlasov-Poisson equations as the semiclassical limit of the Schr\"{o}dinger-Poisson Equations: A numerical study (with Shi Jin and Xiaomei Liao), J. Hyperbolic Differ. Equ., 5, 569--587, 2008; [link]
[7]. Computation of the semiclassical limit of the Schr\"{o}dinger equation with phase shift by a level set method (with Shi Jin), J. Sci. Comput., 35,144--169, 2008; [journal]
[6]. A simple model for biological aggregation with asymmetric sensing (with Paul A. Milewski), Commun. Math. Sci., 6, 397--416, 2008; [journal]
[5]. Computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit (with Shi Jin and Xiaomei Liao), SIAM J. Sci. Comput., 30, 1992--2017, 2008; [journal]
[4]. A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface (with Shi Jin and Guangwei Yuan), Kinet. Relat. Models,1, 65--84, 2008; [journal]
[3]. Numerical study of a domain decomposition method for a two-scale linear transport equation (with Francois Golse, Zhongyi Huang and Shi Jin), Netw. Heterog. Media, 1, 143--166, 2006; [journal]
[2]. On the forward and inverse displacement of spatial parallel manipulators (with Jingshan Zhao, Liang Zhu, Zhijing Feng and Kai Zhou), Int. J. Adv. Manuf. Technol., 29, 1284--1294, 2006; [journal]
[1]. Wavelet-Galerkin method for reaction-diffusion equation (with Zhongyi Huang and Liang Zhu), J. Tsinghua Univ., 46, 392--395, 2006, (in Chinese).