Research Area

· Mathematical Analysis and Numerical Computation for Topological Materials

· Machine-learning-based Mathematical Modeling

· Non-equilibrium Thermodynamics: Conservation-Dissipation Formalism

· Nonlinear Wave Motion

Education

2008  Ph.D. in Mathematics   Tsinghua University, China

2003  B.S.   in Mathematics   Tsinghua University, China

Position

2024–present  Professor, Yau Mathematical Sciences Center, Tsinghua University

2020–2024  Associate Professor, Yau Mathematical Sciences Center, Tsinghua University

2011–2019  Associate Professor, Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University

2008–2011 Instructor & Postdoctoral Researcher, Department of Applied Mathematics, University of Colorado-Boulder

Publications

• Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data(with L. Lu Z. Zeng, Y. Jiang and P. Hu),arXiv:2209.02628

• Traveling edge states in massive Dirac equations along slowly varying edges (with P. Hu and P. Xie), arXiv:2202.13653

• Identification of hydrodynamic instability by convolutional neural networks (with W. Yang, L. Peng and L. Hong), arXiv:2006.01446

• Generalized hydrodynamics and the classical hydrodynamic limit (with Z. Yang and W.-A.Yong), arXiv: 1809.01611

• A rigorous derivation of multicomponent diffusion laws (with Z. Yang and W.-A.Yong), arXiv:1502.03516

• Integrable nonlocal derivative nonlinear Schrödinger equations (with M. Ablowitz, X. Luo and Z. Musslimani), Inverse Problems 38 (2022), 065003

• Three-fold Weyl points in the Schrödinger operator with periodic potentials (with H. Guo and M. Zhang), SIAM Math. Anal. 54 (2022), 3654-3695

• Revealing hidden dynamics from time-series data by ODENet (with P. Hu, W. Yang, L. Hong), J. Comp. Phys., 465(2022), 111203

• Unfitted Nitsche’s method for computing wave modes in topological materials (with H. Guo and X. Yang), J. Sci. Comput. 88 (2021), 24

• Unfitted Nitsche’s method for computing band structures in phononic crystals with impurities (with H. Guo and X. Yang), Comput. Methods Appl. Mech.Engrg. 380 (2021), 113743

• Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential (with P. Xie), (SIAM) Multiscale. Model. Simul. 19 (2021), 951-979

• When machine learning meets multiscale modeling in chemical reactions (with W. Yang, L. Peng and L. Hong), J. Chem. Phys. 153 (2020), 094117

• Linear and nonlinear wave dynamics in modulated honeycomb media (with P. Hu and L. Hong), Stud. Appl. Math. 144 (2020), 18-45

• Wave-packet dynamics in slowly modulated photonic graphene (with P. Xie), J. Differential Equations 267 (2019), 5775-5808

• Elliptic operators with honeycomb symmetry: Dirac points, edge states and applications to photonic graphene (with J. P. Lee-Thorp and M. I. Weinstein), Arch.Rational Mech. Anal. 232 (2019), 1-63

• Bloch theory-based gradient recovery method for computation of edge mode in photonic graphene (with H. Guo and X. Yang), J. Comp. Phys. 379 (2019),403-420

• Generalized Onsager’s reciprocal relations for the master and Fokker-Planck equations (with L. Peng and L. Hong), Phys. Rev. E 97 (2018), 062123

• The Markov process admits a consistent steady-state thermodynamic formalism (with L. Peng and L. Hong), J. Math. Phys. 59 (2018), 013302

• Local bifurcation of electrohydrodynamic waves on a conducting fluid (with Z. Lin and Z. Wang), Phys. Fluids 29 (2017), 032107

• Transport properties in the photonic super-honeycomb lattice–a hybrid fermionic and bosonic system (with H. Zhong, Y. Zhang, et al), Ann. Phys. 529 (2017),1600258

• Novel dissipative properties of the master equation (with L. Hong, J. Chen and W.-A. Yong), J. Math. Phys. 57 (2016), 103303

• PT symmetry in a fractional Schrödinger equation (with Y. Zhang, H. Zhong, M. R. Belic et al), Laser Photon. Rev. 10(2016), 526-531

• A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies (with L. Hong,Z. Yang and W.-A. Yong), J. Non-Equil Thermodynamics 40 (2015), 247-256

• Conservation-dissipation formalism for non-equilibrium thermodynamics (with L. Hong, Z. Yang and W.-A. Yong), J. Non-Equil Thermodynamics 40 (2015),67-74

• Dynamics in PT-symmetric honeycomb lattices with nonlinearity (with C. W. Curtis), Stud. Appl. Math. 135 (2015), 139-170

• Unveiling pseudospin and angular momentum in photonic graphene (with D. Song, V. Paltoglou et al), Nat. Commun. 6 (2015), 6272

• Direct observation of pseudospin-mediated vortex generation in photonic graphene (D. Song, L. Tang, S. Liu, et al), In CLEO:EELS Fundamental Science,2014

• Nonlinear wave packets in deformed honeycomb lattices (with M. J. Ablowitz), SIAM J. Appl. Math. 73 (2013), 1959-1979

• Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices (with M. J. Ablowitz), in book ”Spontaneous Symmetry Breaking, Self-Trapping, and Josephson

Oscillations” Progress in Optical Science and Photonics 1 (2013), 1-26

• Localized nonlinear edge states in honeycomb lattices (with M. J. Ablowitz and C. W. Curtis), Phys. Rev. A 88 (2013), 13850.

• Unified orbital description of the envelope dynamics in two-dimensional simple periodic lattices (with M. J. Ablowitz), Stud. Appl. Math. 131 (2013),41-71

• Nonlinear dynamics of wave packets in parity-time-symmetric optical lattices near the phase transition point (with S.D. Nixon and J. Yang), Opt. Lett. 37 (2012),4874-4876

• On Tight binding approximations in optical lattice (with M. J. Ablowitz and C. W. Curtis), Stud. Appl. Math. 129 (2012),362-388

• Nonlinear waves in shallow honeycomb lattices (with M. J. Ablowitz), SIAM J. Appl. Math. 72 (2012) 240-260

• Scalable Misbehavior Detection in Online Video Chat Services (with X. Xing, Y. Liang, et al), Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining 2012, 552-560

• Nonlinear diffraction in photonic graphene (with M. J. Ablowitz), Opt. Lett. 36 (2011), 762-3764

• Nonlinear wave dynamics: from lasers to fluids (with M. J. Ablowitz, T. S. Haut, T. P. Horikis and S. D. Nixon), Discrete Contin. Dyn. Syst. S 4 (2011), 923- 955

• Evolution of Bloch-mode envelopes in two-dimensional generalized honeycomb lattices (with M. J. Ablowitz),Phys. Rev. A 82 (2010), 013840

• Conical diffraction in honeycomb lattices (with M.J. Ablowitz and S. D. Nixon), Phys. Rev. A 79 (2009), 053830

• Asymptotic analysis of pulse dynamics in mode-locked lasers (with M. J. Ablowitz, T. P. Horikis and S. D. Nixon), Stud. Appl. Math. 122 (2009), 411-425

• Separatrix map analysis for fractal scatterings in weak solitary wave interactions (with J. Yang and R. Haberman), Stud. Appl. Math. 122 (2009), 449-483

• A universal separatrix map for weak interactions of solitary waves in generalized nonlinear Schrödinger equations (with J. Yang and R. Haberman), Physica D237 (2008), 2411-2422

• Universal map for fractal structures in weak interactions of solitary waves (with J. Yang and R. Haberman), Phys. Rev. Lett. 100(2008), 143901

• Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations (with J. Yang), Phys. Rev. E 75 (2007), 036605