Lexing Ying

Professor, Department of Mathematics

Member, Institute for Computational and Mathematical Engineering

Stanford University

I am on sabbatical at Facebook AI Research.

Phone: 650-723-2221

Email: lexing at stanford dot edu

Address:

Department of Mathematics

450 Serra Mall, Bldg 380, Rm 382X

Stanford University

Stanford, CA 94305-2125

[CV 12/2017]， [中文简历 05/2018]

The webpages of my current courses are hosted at canvas.stanford.edu

- Morningside Silver Medal of Applied Mathematics, ICCM, 2016.
- James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, SIAM, 2013.
- Feng Kang Prize of Scientific Computing, Chinese Academy of Sciences, 2011.
- CAREER Award, National Science Foundation, 2009.
- Alfred P. Sloan Research Fellowship, 2007.

PhD students

- Jing An [Link] (co-advised with Lenya Ryzhik)
- Philip Etter
- Jordi Feliu Faba [Link]
- Cindy Catherine Orozco Bohorquez [Link]

- Fei Liu
- Victor Minden [Link]
- Yingzhou Li [Link]
- Anil Damle [Link]
- Kenneth Ho [Link]
- Haizhao Yang [Link]
- Jack Poulson [Link]
- Jingwei Hu [Link]
- Paul Tsuji
- Phillip Schmitz

Preprints

- Yuehaw Khoo and Lexing Ying. SwitchNet: a neural network model for forward and inverse scattering problems. [PDF]
- Yuwei Fan, Cindy Orozco Bohorquez, and Lexing Ying. BCR-Net: a neural network based on the nonstandard wavelet form. [PDF]
- Yuehaw Khoo and Lexing Ying. Convex relaxation approaches for strictly correlated density functional theory. [PDF]
- Yuwei Fan, Jordi Feliu-Faba, Lin Lin, Lexing Ying, and Leonardo Zepeda-Nunez. A multiscale neural network based on hierarchical nested bases. [PDF]
- Jordi Feliu-Faba, Kenneth Ho, and Lexing Ying, Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations. [PDF]
- Yuwei Fan, Lin Lin, Lexing Ying, and Leonardo Zepeda-Nunez, A multiscale neural network based on hierarchical matrices. [PDF]
- Jing An, Jianfeng Lu, and Lexing Ying, Stochastic modified equations for the asynchronous stochastic gradient descent. [PDF]
- Victor Minden and Lexing Ying. A simple solver for the fractional Laplacian in multiple dimensions. [PDF]
- Yuwei Fan, Jing An, and Lexing Ying. Fast algorithms for integral formulations of steady-state radiative transfer equation. [PDF]
- Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Efficient construction of tensor ring representations from sampling. Submitted. [PDF]
- Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Solving PDE problems with uncertainty using neural-networks. Submitted. [PDF]

- Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Solving for high dimensional committor functions using artificial neural networks. To appear in RMS. [PDF]
- Fei Liu and Lexing Ying, Sparsifying preconditioner for the time-harmonic Maxwell’s equations. To appear in JCP. [PDF]
- Zhenning Cai, Yuwei Fan, and Lexing Ying. An entropic Fourier method for the Boltzmann equation. SIAM J. Sci. Comput. 40(5) (2018). [PDF]
- Anil Damle, Victor Minden, and Lexing Ying. Robust and efficient multi-way spectral clustering. To appear in Information and Inference. [PDF]
- Fei Liu and Lexing Ying. Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation. To appear in SIAM Journal on Scientific Computing. [PDF]
- Anil Damle, Lin Lin, and Lexing Ying. Computing localized representations of the kohn-sham subspace via randomization and refinement. To appear in SIAM Journal on Scientific Computing. [PDF]
- Victor Minden, Anil Damle, Kenneth Ho, and Lexing Ying. Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. SIAM Journal of Multiscale Modeling and Simulation 15-4 (2017). [PDF]
- Lexing Ying. Tensor network skeletonization. SIAM Journal of Multiscale Modeling and Simulation 15-4 (2017). [PDF]
- Yingzhou Li, Haizhao Yang, and Lexing Ying. Multidimensional butterfly factorization. To appear in Applied and Computational Harmonic Analysis. [PDF]
- Yingzhou Li and Lexing Ying. Distributed-memory hierarchical interpolative factorization. Research in Mathematical Sciences 4 (2017). [PDF]
- Fei Liu and Lexing Ying. Localized sparsifying preconditioner for periodic indefinite systems. Communications in Mathematical Sciences 15-4 (2017). [PDF]
- Victor Minden, Kenneth Ho, Anil Damle, and Lexing Ying. A recursive skeletonization factorization based on strong admissibility. SIAM Multiscale Modeling and Simulation 15-2 (2017). [PDF]
- Lin Lin, Ze Xu, and Lexing Ying. Adaptively compressed polarizability operator for accelerating large scale ab initio phonon calculations. SIAM Multiscale Modeling and Simulation 15-1 (2017). [PDF]
- Anil Damle, Lin Lin, and Lexing Ying. SCDM-k: Localized orbitals for solids via selected columns of the density matrix. Journal of Computational Physics 334 (2017). [PDF]
- Jianfeng Lu and Lexing Ying, Fast algorithm for periodic density fitting for Bloch waves. Annals of Mathematical Sciences and Applications 1-2 (2016). [PDF]
- Jianfeng Lu and Lexing Ying, Sparsifying preconditioner for soliton calculations. Journal of Computational Physics 315 (2016). [PDF]
- Fei Liu and Lexing Ying. Additive sweeping preconditioner for the Helmholtz equation. SIAM Multiscale Modeling and Simulation 14-2 (2016). [PDF]
- Fei Liu and Lexing Ying. Recursive sweeping preconditioner for the 3D Helmholtz equation. SIAM Journal on Scientific Computing 38-2 (2016). [PDF]
- Victor Minden, Anil Damle, Kenneth Ho, and Lexing Ying. A technique for updating hierarchical factorizations of integral operators. SIAM Multiscale Modeling and Simulation 14-1 (2016). [PDF]
- Junzhe Sun, Sergey Fomel, and Lexing Ying. Lowrank one-step wave extrapolation for reverse-time migration. Geophysics 81-1 (2016).
- Kenneth Ho and Lexing Ying. Hierarchical interpolative factorization for elliptic operators: differential equations. Communications in Pure and Applied Mathematics 69-8 (2016). [PDF]
- Kenneth Ho and Lexing Ying. Hierarchical interpolative factorization for elliptic operators: integral equations. Communications in Pure and Applied Mathematics 69-7 (2016). [PDF]
- Haizhao Yang, Jianfeng Lu, and Lexing Ying. Crystal image analysis using 2D synchrosqueezed transforms. SIAM Multiscale Modeling and Simulation 13-4 (2015). [PDF]
- Jianfeng Lu and Lexing Ying. Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Journal of Computational Physics 302-1 (2015). [PDF]
- Lexing Ying. Directional preconditioner for 2D high frequency obstacle scattering. SIAM Multiscale Modeling and Simulation 13-3 (2015). [PDF]
- Haizhao Yang, Jianfeng Lu, W. Brown, I. Daubechies, and Lexing Ying. Quantitative canvas weave analysis using 2D synchrosqueezed transforms. IEEE Signal Processing Magazine 55 (2015). [PDF]
- Yingzhou Li, Haizhao Yang, Eileen Martin, Kenneth Ho, and Lexing Ying. Butterfly factorization. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- Lexing Ying. Sparsifying preconditioner for the Lippmann-Schwinger equation. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- Yingzhou Li, Haizhao Yang, and Lexing Ying. A multiscale butterfly algorithm for multidimensional Fourier integral operators. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- Anil Damle, Lin Lin, and Lexing Ying. Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix. J. Chem. Theory Comput. 11 (2015) [PDF]
- Lexing Ying. Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- Lexing Ying. Fast directional computation of high frequency boundary integrals via local FFTs. SIAM Multiscale Modeling and Simulation 13-1 (2015). [PDF]
- Jingwei Hu and Lexing Ying, A fast algorithm for the energy space boson Boltzmann collision operator. Mathematics of Computation 84 (2015). [PDF]
- Jingwei Hu, Sergey Fomel, and Lexing Ying. A fast algorithm for 3D azimuthally anisotropic velocity scan. Geophysical Prospecting 63 (2015). [PDF]
- Anil Damle, Lin Lin, and Lexing Ying. Pole expansion for solving a type of parametrized linear systems in electronic structure calculations. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- Austin Benson, Jack Poulson, Khoa Tran, Bjorn Engquist, and Lexing Ying. A parallel directional fast multipole method. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- Haizhao Yang and Lexing Ying, Synchrosqueezed curvelet transform for two-dimensional mode decomposition. SIAM Journal on Mathematical Analysis 46 (2014). [PDF]
- Jack Poulson, Laurent Demanet, Nicholas Maxwell, and Lexing Ying. A parallel butterfly algorithm. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- Paul Tsuji, Jack Poulson, Bjorn Engquist, and Lexing Ying. Sweeping preconditioners for elastic wave propagation with spectral element methods. ESAIM: Mathematical Modeling and Numerical Analysis 48 (2014). [PDF]
- Phillip Schmitz and Lexing Ying. A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices. Journal of Computational Physics 258 (2014). [PDF]
- Haizhao Yang and Lexing Ying. Synchrosqueezed wave packet transform for 2D mode decomposition. SIAM Journal on Imaging Sciences 6 (2014). [PDF]
- Jingwei Hu, Sergey Fomel, Laurent Demanet, and Lexing Ying. A fast butterfly algorithm for the hyperbolic Radon transform. Geophysics 78 (2013). [PDF]
- Jack Poulson, Bjorn Engquist, S. Li and Lexing Ying. A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. SIAM Journal on Scientific Computing 35 (2013). [PDF]
- X. Song, Sergey Fomel, and Lexing Ying. Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation. Geophysical Journal International 193 (2013). [PDF]
- G. Bao, J. Qian, Lexing Ying, and H. Zhang. A convergent multiscale Gaussian-beam parametrix for wave equations. Communications in Partial Differential Equations 38 (2013). [PDF]
- Bjorn Engquist and Lexing Ying. A fast algorithm for reiterated homogenization. Communications in Mathematical Sciences 11 (2013). [PDF]
- Sergey Fomel, Lexing Ying, and X. Song. Seismic wave extrapolation using lowrank symbol approximation. Geophysical Prospecting 61 (2013). [PDF]
- Lin Lin and Lexing Ying. Element orbitals for Kohn-Sham density functional theory. Physical Review B 85 (2012). [PDF]
- I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, Lexing Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. Communications of the ACM 55 (2012). [PDF]
- Lin Lin, Jianfeng Lu, Lexing Ying, and Weinan E. Optimized local basis set for Kohn-Sham density functional theory. Journal of Computational Physics 231 (2012). [PDF]
- Haizhao Yang and Lexing Ying. A fast algorithm for multilinear operators. Applied and Computational Harmonic Analysis 33 (2012). [PDF]
- Lexing Ying. A pedestrian introduction to fast multipole methods. Science China Mathematics 55 (2012). [PDF]
- Laurent Demanet and L. Ying. Fast wave computation via Fourier integral operators. Mathematics of Computation 81 (2012). [PDF]
- Paul Tsuji, Bjorn Engquist, and Lexing Ying. A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements. Journal of Computational Physics 231 (2012). [PDF]
- Paul Tsuji and Lexing Ying. A sweeping preconditioner for Yee's finite difference approximation of time-harmonic Maxwell's equations. Frontiers of Mathematics in China 7 (2012). [PDF]
- Lin Lin, Jianfeng Lu, Lexing Ying, and Weinan E. Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation. Journal of Computational Physics 231 (2012). [PDF]
- Laurent Demanet, M. Ferrara, N. Maxwell, Jack Poulson, and Lexing Ying. A butterfly algorithm for synthetic aperture radar imaging. SIAM Journal on Imaging Sciences 5 (2012). [PDF]
- Jingwei Hu and Lexing Ying. A fast spectral algorithm for the quantum Boltzmann collision operator. Commun. Math. Sci 10 (2012). [PDF]
- Phillip Schmitz and Lexing Ying. A fast direct solver for elliptic problems on general meshes in 2D. Journal of Computational Physics 231 (2012). [PDF]
- Shidong Jiang, Bo Ren, Paul Tsuji, and Lexing Ying. Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions. Journal of Computational Physics 230 (2011). [PDF]
- Bjorn Engquist and Lexing Ying. Sweeping preconditioner for the Helmholtz equation: Moving perfectly matched layers. SIAM Multiscale Modeling and Simulation 9 (2011). [PDF]
- Lin Lin, Chao Yang, Jianfeng Lu, Lexing Ying, and Weinan E. A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM Journal on Scientific Computing 33 (2011). [PDF]
- Lin Lin, Jianfeng Lu, and Lexing Ying. Fast construction of hierarchical matrix representation from matrix-vector multiplication. Journal of Computational Physics 230 (2011). [PDF]
- Paul Tsuji and Lexing Ying. A fast directional algorithm for high-frequency electromagnetic scattering. Journal of Computational Physics 230 (2011). [PDF]
- Bjorn Engquist and Lexing Ying. Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation. Communications in Pure and Applied Mathematics 64 (2011). [PDF]
- Lin Lin, C. Yang, Juan Meza, Jianfeng Lu, Lexing Ying, and Weinan E. SelInv--an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Software 37 (2011). [PDF]
- Paul Tsuji, Dongbin Xiu, and Lexing Ying. A fast method for high-frequency acoustic scattering from random scatterers. International Journal on Uncertainty Quantification 1 (2011). [PDF]
- Laurent Demanet and Lexing Ying. Discrete symbol calculus. SIAM Rev. 53 (2011). [PDF]
- Jianliang Qian and Lexing Ying. Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. SIAM Multiscale Modeling and Simulation 8 (2010). [PDF]
- Jianliang Qian and Lexing Ying. Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation. J. Computational Physics 229 (2010). [PDF]
- Laurent Demanet and Lexing Ying. Scattering in flatland: efficient representations via wave atoms. Found. of Comput. Math. 10 (2010). [PDF]
- Bjorn Engquist and Lexing Ying. Fast directional algorithms for the Helmholtz kernel. Journal of Computational and Applied Mathematics 234 (2010). [PDF]
- Lin Lin, Jianfeng Lu, Lexing Ying, and Weinan E. Pole-based approximation of the Fermi-Dirac function. Chinese Annals of Mathematics - Series B 30 (2009). [PDF]
- Lexing Ying and Sergey Fomel. Fast computation of partial Fourier transforms. SIAM Multiscale Modeling and Simulation 8 (2009). [PDF]
- Lin Lin, Jianfeng Lu, Lexing Ying, Roberto Car, and Weinan E. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Commun. Math. Sci. 7 (2009). [PDF]
- Emmanuel Candes, Laurent Demanet and Lexing Ying. A fast butterfly algorithm for the computation of Fourier integral operators. SIAM Multiscale Modeling and Simulation 7 (2009). [PDF]
- Bjorn Engquist and Lexing Ying. A fast directional algorithm for high frequency acoustic scattering in two dimension. Communications in Mathematical Sciences 7 (2009). [PDF]
- Laurent Demanet and Lexing Ying. Wave atoms and time upscaling of wave equations. Numerische Mathematik 113 (2009). [PDF]
- Lexing Ying. Sparse Fourier transform via butterfly algorithm. SIAM Journal on Scientific Computing 31 (2009). [PDF]
- Laurent Demanet and Lexing Ying. Wave atoms and sparsity of oscillatory patterns. Applied and Computational Harmonic Analysis 23 (2007). [PDF]
- Emmanuel Candes, Laurent Demanet and Lexing Ying. Fast computation of Fourier integral operators. SIAM Journal on Scientific Computing 29 (2007). [PDF]
- Bjorn Engquist and Lexing Ying. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal on Scientific Computing 29 (2007). [PDF]
- Lexing Ying and Emmanuel Candes. The phase flow method. Journal of Computational Physics 220 (2006). [PDF]
- Lexing Ying and Emmanuel Candes. Fast geodesics computation with the phase flow method. Journal of Computational Physics 220 (2006). [PDF]
- Lexing Ying, George Biros, and Denis Zorin. A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Journal of Computational Physics 219 (2006). [PDF]
- Emmanuel Candes, Laurent Demanet, Donoho Donoho, and Lexing Ying. Fast discrete curvelet transforms. SIAM Multiscale Modeling and Simulation 5 (2006). [PDF]
- Lexing Ying. A kernel independent fast multipole algorithm for radial basis functions. Journal of Computational Physics 213 (2006). [PDF]
- Lexing Ying and Denis Zorin. A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23 (2004) (SIGGRAPH 2004). [PDF]
- Lexing Ying, George Biros, and Denis Zorin. A kernel-independent adaptive fast multipole method in two and three dimensions. Journal of Computational Physics 196 (2004). [PDF]
- George Biros, Lexing Ying, and Denis Zorin. A fast solver for the Stokes equations with distributed forces in complex geometries. Journal of Computational Physics 194 (2004). [PDF]
- L. Velho, K. Perlin, Lexing Ying, and H. Biermann. Algorithmic shape modeling with subdivision surfaces. Computers and Graphics 26 (2002). [PDF]

- Jingwei Hu, Sergey Fomel, and Lexing Ying, A fast algorithm for 3D azimuthally anisotropic velocity scan. Proceedings of the 2013 SEG Annual Meeting.
- Jingwei Hu, Sergey Fomel, Laurent Demanet, and Lexing Ying, A fast butterfly algorithm for the hyperbolic Radon transform. Proceedings of the 2012 SEG Annual Meeting.
- Jack Poulson, Bjorn Engquist, S. Li, and Lexing Ying, A parallel sweeping preconditioner for frequency-domain seismic wave propagation. Proceedings of the 2012 SEG Annual Meeting.
- X. Song, Sergey Fomel, Lexing Ying, and T. Ding, Lowrank finite-difference for wave extrapolation. Proceedings of the 2011 SEG Annaul Meeting.
- Bjorn Engquist, Jack Poulson, and Lexing Ying, Sweeping preconditioner for the 3D Helmholtz equation. Proceedings of the 2011 SEG Annaul Meeting.
- Sergey Fomel, Lexing Ying, and X. Song, Seismic wave extrapolation using lowrank symbol approximation. Proceedings of the 2010 SEG Annaul Meeting.
- I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, Lexing Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. Proceedings of Proc. ACM/IEEE Conf. Supercomputing (SC), Portland, OR, USA, 2009. This paper is nominated for the Best Technical Paper Award. [PDF]
- Bjorn Engquist, Khoa Tran, and Lexing Ying. Fast hybrid algorithms for high frequency scattering Engquist. The 3rd Conference on Mathematical Modeling of Wave Phenomena and the 20th Nordic Conference on Radio Science and Communications. AIP Conference Proceedings, Volume 1106, pp. 3-17 (2009).
- Laurent Demanet and Lexing Ying. Curvelets and wave atoms for mirror-extended images. Proc. SPIE Wavelets XII conf, San Diego, August 2007 (Invited Paper). [PDF]
- Lexing Ying, Laurent Demanet, and Emmanuel Candes. 3D discrete curvelet transform. Proc. Wavelets XI conf., San Diego, July 2005 (Invited Paper). [PDF]
- Lexing Ying, George Biros, Denis Zorin, and H. Langston. A new parallel kernel-independent fast multipole method. Proceedings of the 2003 ACM/IEEE conference on Supercomputing, 14-29, 2003. This paper was awarded the Best Student Paper Award and nominated for the Gordon Bell Award and the Best Technical Paper Award. [PDF]
- George Biros, Lexing Ying, Denis Zorin. The embedded boundary integral equation solver for the incompressible Navier-Stokes equations. International Association for Boundary Element Methods Symposium, 2002. [PDF]
- Lexing Ying, Denis Zorin. Nonmanifold subdivision. The 12th IEEE Visualization Conference, 2001. [PDF]
- Lexing Ying, A. Hertzmann, H. Biermann, Denis Zorin. Texture and shape synthesis on surfaces. The 12th Eurographics Workshop on Rendering, 2001. [PDF]

- Bjorn Engquist and Lexing Ying, Fast algorithms for high frequency wave propagation. To appear in Numerical Analysis of Multiscale Problems, I. Graham, T. Hou, O. Lakkis and R. Scheichl (editors), Lecture Notes in Computational Science and Engineeering, Springer.
- Lexing Ying. Fast algorithms boundary integral equations. In Bjorn Engquist, O. Runborg, P. Lotstedt, editors, Multiscale Methods in Science and Engineering, pages 139-194, volume 66 of Lecture Notes in Computational Science and Engineering, Heidelberg, 2009. Springer Verlag. [PDF]

- Anshul Gupta and Lexing Ying. A Fast Maximum-Weight-Bipartite-Matching Algorithm for Reducing Pivoting in Sparse Gaussian Elimination. Technical report RC 21576 (97320), IBM T. J. Watson Research Center, Yorktown Heights, NY, 1999. [PDF]

- Sweeping preconditioner [Code]
- Additive sweeping preconditioner [Code]
- Recursive sweeping preconditioner [Code]
- 1D synchrosqueezed wave packet transforms [Code]
- Multiscale Butterfly Algorithm [Code]
- Butterfly factorization [Code]
- ButterflyLab [Code]
- Directional FMM (3D parallel) for Helmholtz Equation [Code]
- Directional FMM (3D sequential) for Helmholtz Equation [Code]
- Directional FMM (2D sequential) for Helmholtz Equation [Code]
- Wave atom transforms [Code]
- Fast discrete Curvelet transform [Code]
- Manifold-based surface construction of arbitrary smoothness [Code]
- Kernel independent fast multipole method [Code]