Lexing Ying's Profile | Stanford Profiles

Academic Appointments

Professor, Mathematics
Member, Institute for Computational and Mathematical Engineering (ICME)

Honors & Awards

SIAM Fellow, SIAM (2024)
Invited lecture, The International Congress of Mathematicians (2022)
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, Sloan Foundation (2007)

Contact

Academic
lexing@stanford.edu

University - Faculty Department: Mathematics Position: Professor of Mathematics

Additional Info

Mail Code: 2125

2023-24 Courses

Computational Methods of Applied Mathematics
CME 306, MATH 220B (Win)
Introduction to Scientific Computing
CME 108 (Aut)
Topics in Applied Math II
MATH 275B (Win)
Independent Studies (5)
- Advanced Reading and Research
  MATH 360 (Aut, Win, Spr, Sum)
- Curricular Practical Training
  CME 390 (Sum)
- Master's Research
  CME 291 (Spr)
- Ph.D. Research
  CME 400 (Aut, Win, Spr, Sum)
- Ph.D. Research Rotation
  CME 391 (Aut, Win, Spr)
Prior Year Courses
2022-23 Courses
- Linear Algebra, Multivariable Calculus, and Modern Applications
  MATH 51 (Win)
- Numerical Solution of Partial Differential Equations
  CME 306, MATH 226 (Spr)
2021-22 Courses
- Basic Probability and Stochastic Processes with Engineering Applications
  CME 298, MATH 158 (Spr)
- Numerical Solution of Partial Differential Equations
  CME 306, MATH 226 (Spr)
- Topics in Applied Math I
  MATH 275A (Aut)
2020-21 Courses
- Applied Matrix Theory
  MATH 104 (Aut)
- Basic Probability and Stochastic Processes with Engineering Applications
  CME 298, MATH 158 (Spr)
- Numerical Solution of Partial Differential Equations
  CME 306, MATH 226 (Spr)

Stanford Advisees

Doctoral Dissertation Reader (AC)
Daniel Paul Kunin, Rahul Sarkar
Doctoral Dissertation Advisor (AC)
Rajat Dwaraknath, Yinuo Ren, Xun Tang
Doctoral Dissertation Co-Advisor (AC)
Ya-Chi Chu, Milo Marsden

All Publications

Meta-learning pseudo-differential operators with deep neural networks JOURNAL OF COMPUTATIONAL PHYSICS Feliu-Faba, J., Fan, Y., Ying, L. 2020; 408

View details for DOI 10.1016/j.jcp.2020.109309

View details for Web of Science ID 000521731200026
Solving electrical impedance tomography with deep learning JOURNAL OF COMPUTATIONAL PHYSICS Fan, Y., Ying, L. 2020; 404

View details for DOI 10.1016/j.jcp.2019.109119

View details for Web of Science ID 000507854200027
Hessian transport gradient flows RESEARCH IN THE MATHEMATICAL SCIENCES Li, W., Ying, L. 2019; 6 (4)

View details for DOI 10.1007/s40687-019-0198-9

View details for Web of Science ID 000509100300001
BCR-Net: A neural network based on the nonstandard wavelet form JOURNAL OF COMPUTATIONAL PHYSICS Fan, Y., Bohorquez, C., Ying, L. 2019; 384: 1–15

View details for DOI 10.1016/j.jcp.2019.02.002

View details for Web of Science ID 000460888400001
A multiscale neural network based on hierarchical nested bases RESEARCH IN THE MATHEMATICAL SCIENCES Fan, Y., Feliu-Faba, J., Lin, L., Ying, L., Zepeda-Nunez, L. 2019; 6 (2)

View details for DOI 10.1007/s40687-019-0183-3

View details for Web of Science ID 000464654500001
Simple, direct and efficient multi-way spectral clustering INFORMATION AND INFERENCE-A JOURNAL OF THE IMA Damle, A., Minden, V., Ying, L. 2019; 8 (1): 181–203

View details for DOI 10.1093/imaiai/iay008

View details for Web of Science ID 000469774500006
Fast algorithms for integral formulations of steady-state radiative transfer equation JOURNAL OF COMPUTATIONAL PHYSICS Fan, Y., An, J., Ying, L. 2019; 380: 191–211

View details for DOI 10.1016/j.jcp.2018.12.014

View details for Web of Science ID 000458145900009
Sparsifying preconditioner for the time-harmonic Maxwell's equations JOURNAL OF COMPUTATIONAL PHYSICS Liu, F., Ying, L. 2019; 376: 913–23

View details for DOI 10.1016/j.jcp.2018.10.004

View details for Web of Science ID 000450337400042
CONVEX RELAXATION APPROACHES FOR STRICTLY CORRELATED DENSITY FUNCTIONAL THEORY SIAM JOURNAL ON SCIENTIFIC COMPUTING Khoo, Y., Ying, L. 2019; 41 (4): B773–B795

View details for DOI 10.1137/18M1207478

View details for Web of Science ID 000483924100032
Numerical methods for Kohn-Sham density functional theory ACTA NUMERICA Lin, L., Lu, J., Ying, L. 2019; 28: 405–539

View details for DOI 10.1017/S0962492919000047

View details for Web of Science ID 000491992100004
SWITCHNET: A NEURAL NETWORK MODEL FOR FORWARD AND INVERSE SCATTERING PROBLEMS SIAM JOURNAL ON SCIENTIFIC COMPUTING Khoo, Y., Ying, L. 2019; 41 (5): A3182–A3201

View details for DOI 10.1137/18M1222399

View details for Web of Science ID 000493897100019
SPARSIFY AND SWEEP: AN EFFICIENT PRECONDITIONER FOR THE LIPPMANN- SCHWINGER EQUATION SIAM JOURNAL ON SCIENTIFIC COMPUTING Liu, F., Ying, L. 2018; 40 (2): B379–B404

View details for DOI 10.1137/17M1132057

View details for Web of Science ID 000431100400028
AN ENTROPIC FOURIER METHOD FOR THE BOLTZMANN EQUATION SIAM JOURNAL ON SCIENTIFIC COMPUTING Cai, Z., Fan, Y., Ying, L. 2018; 40 (5): A2858–A2882

View details for DOI 10.1137/17M1127041

View details for Web of Science ID 000448803100003
SCDM-k: Localized orbitals for solids via selected columns of the density matrix JOURNAL OF COMPUTATIONAL PHYSICS Damle, A., Lin, L., Ying, L. 2017; 334: 1-15

View details for DOI 10.1016/j.jcp.2016.12.053

View details for Web of Science ID 000395210500001
ADAPTIVELY COMPRESSED POLARIZABILITY OPERATOR FOR ACCELERATING LARGE SCALE AB INITIO PHONON CALCULATIONS MULTISCALE MODELING & SIMULATION Lin, L., Xu, Z., Ying, L. 2017; 15 (1): 29-55

View details for DOI 10.1137/16M1077325

View details for Web of Science ID 000398614800002
COMPUTING LOCALIZED REPRESENTATIONS OF THE KOHN-SHAM SUBSPACE VIA RANDOMIZATION AND REFINEMENT SIAM JOURNAL ON SCIENTIFIC COMPUTING Damle, A., Lin, L., Ying, L. 2017; 39 (6): B1178–B1198

View details for DOI 10.1137/16M1098589

View details for Web of Science ID 000418659900007
TENSOR NETWORK SKELETONIZATION MULTISCALE MODELING & SIMULATION Ying, L. 2017; 15 (4): 1423–47

View details for DOI 10.1137/16M1082676

View details for Web of Science ID 000418691000005
Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Ho, K. L., Ying, L. 2016; 69 (8): 1415-1451

View details for DOI 10.1002/cpa.21582

View details for Web of Science ID 000379919000001
Hierarchical Interpolative Factorization for Elliptic Operators: Integral Equations COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Ho, K. L., Ying, L. 2016; 69 (7): 1314-1353

View details for DOI 10.1002/cpa.21577

View details for Web of Science ID 000379917800003
Sparsifying preconditioner for soliton calculations JOURNAL OF COMPUTATIONAL PHYSICS Lu, J., Ying, L. 2016; 315: 458-466

View details for DOI 10.1016/j.jcp.2016.03.061

View details for Web of Science ID 000374832700025
RECURSIVE SWEEPING PRECONDITIONER FOR THE THREE-DIMENSIONAL HELMHOLTZ EQUATION SIAM JOURNAL ON SCIENTIFIC COMPUTING Liu, F., Ying, L. 2016; 38 (2): A814-A832

View details for DOI 10.1137/15M1010154

View details for Web of Science ID 000375484800009
A TECHNIQUE FOR UPDATING HIERARCHICAL SKELETONIZATION-BASED FACTORIZATIONS OF INTEGRAL OPERATORS MULTISCALE MODELING & SIMULATION Minden, V., Damle, A., Ho, K. L., Ying, L. 2016; 14 (1): 42-64

View details for DOI 10.1137/15M1024500

View details for Web of Science ID 000373366500002
ADDITIVE SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION MULTISCALE MODELING & SIMULATION Liu, F., Ying, L. 2016; 14 (2): 799-822

View details for DOI 10.1137/15M1017144

View details for Web of Science ID 000379356600008
Low-rank one-step wave extrapolation for reverse time migration GEOPHYSICS Sun, J., Fomel, S., Ying, L. 2016; 81 (1): S39-S54

View details for DOI 10.1190/GEO2015-0183.1

View details for Web of Science ID 000377880100046
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost JOURNAL OF COMPUTATIONAL PHYSICS Lu, J., Ying, L. 2015; 302: 329-335

View details for DOI 10.1016/j.jcp.2015.09.014

View details for Web of Science ID 000364256100018
Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms Application of time-frequency analysis to art investigation IEEE SIGNAL PROCESSING MAGAZINE Yang, H., Lu, J., Brown, W. P., Daubechies, I., Ying, L. 2015; 32 (4): 55-63

View details for DOI 10.1109/MSP.2015.2406882

View details for Web of Science ID 000356539400009
Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix. Journal of chemical theory and computation Damle, A., Lin, L., Ying, L. 2015; 11 (4): 1463-9

Abstract

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. We avoid the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the core portion of our localization procedure is not dependent on any adjustable parameters. The only adjustable parameters present pertain to the use of the SCDM after their computation (for example, at what value should the SCDM be truncated). Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining the orthogonalized SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near-linear scaling.

View details for DOI 10.1021/ct500985f

View details for PubMedID 26574357
Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix JOURNAL OF CHEMICAL THEORY AND COMPUTATION Damle, A., Lin, L., Ying, L. 2015; 11 (4): 1463-1469

View details for DOI 10.1021/ct500985f

View details for Web of Science ID 000353176500013
A fast algorithm for 3D azimuthally anisotropic velocity scan GEOPHYSICAL PROSPECTING Hu, J., Fomel, S., Ying, L. 2015; 63 (2): 368-377

View details for DOI 10.1111/1365-2478.12180

View details for Web of Science ID 000349974600007
A FAST ALGORITHM FOR THE ENERGY SPACE BOSON BOLTZMANN COLLISION OPERATOR MATHEMATICS OF COMPUTATION Hu, J., Ying, L. 2015; 84 (291): 271-288

View details for Web of Science ID 000351441400010
DIRECTIONAL PRECONDITIONER FOR 2D HIGH FREQUENCY OBSTACLE SCATTERING MULTISCALE MODELING & SIMULATION Ying, L. 2015; 13 (3): 829-846

View details for DOI 10.1137/140985135

View details for Web of Science ID 000362421000005
CRYSTAL IMAGE ANALYSIS USING 2D SYNCHROSQUEEZED TRANSFORMS MULTISCALE MODELING & SIMULATION Yang, H., Lu, J., Ying, L. 2015; 13 (4): 1542-1572

View details for DOI 10.1137/140955872

View details for Web of Science ID 000367090400017
SPARSIFYING PRECONDITIONER FOR THE LIPPMANN-SCHWINGER EQUATION MULTISCALE MODELING & SIMULATION Ying, L. 2015; 13 (2): 644-660

View details for DOI 10.1137/140985147

View details for Web of Science ID 000357405000010
BUTTERFLY FACTORIZATION MULTISCALE MODELING & SIMULATION Li, Y., Yang, H., Martin, E. R., Ho, K. L., Ying, L. 2015; 13 (2): 714-732

View details for DOI 10.1137/15M1007173

View details for Web of Science ID 000357405000013
FAST DIRECTIONAL COMPUTATION OF HIGH FREQUENCY BOUNDARY INTEGRALS VIA LOCAL FFTs MULTISCALE MODELING & SIMULATION Ying, L. 2015; 13 (1): 423-439

View details for Web of Science ID 000352234400015
SPARSIFYING PRECONDITIONER FOR PSEUDOSPECTRAL APPROXIMATIONS OF INDEFINITE SYSTEMS ON PERIODIC STRUCTURES MULTISCALE MODELING & SIMULATION Ying, L. 2015; 13 (2): 459-471

View details for DOI 10.1137/140985159

View details for Web of Science ID 000357405000001
A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS MULTISCALE MODELING & SIMULATION Li, Y., Yang, H., Ying, L. 2015; 13 (2): 614-631

View details for DOI 10.1137/140997658

View details for Web of Science ID 000357405000008
SWEEPING PRECONDITIONERS FOR ELASTIC WAVE PROPAGATION WITH SPECTRAL ELEMENT METHODS ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE Tsuji, P., Poulson, J., Engquist, B., Ying, L. 2014; 48 (2): 433-447

View details for DOI 10.1051/m2an/2013114

View details for Web of Science ID 000331943800007
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices JOURNAL OF COMPUTATIONAL PHYSICS Schmitz, P. G., Ying, L. 2014; 258: 227-245

View details for DOI 10.1016/j.jcp.2013.10.030

View details for Web of Science ID 000329118500012
A PARALLEL BUTTERFLY ALGORITHM SIAM JOURNAL ON SCIENTIFIC COMPUTING Poulson, J., Demanet, L., Maxwell, N., Ying, L. 2014; 36 (1): C49-C65

View details for DOI 10.1137/130921544

View details for Web of Science ID 000333415500023
POLE EXPANSION FOR SOLVING A TYPE OF PARAMETRIZED LINEAR SYSTEMS IN ELECTRONIC STRUCTURE CALCULATIONS SIAM JOURNAL ON SCIENTIFIC COMPUTING Damle, A., Lin, L., Ying, L. 2014; 36 (6): A2929-A2951

View details for DOI 10.1137/130944825

View details for Web of Science ID 000346838800019
A PARALLEL DIRECTIONAL FAST MULTIPOLE METHOD SIAM JOURNAL ON SCIENTIFIC COMPUTING Benson, A. R., Poulson, J., Tran, K., Engquist, B., Ying, L. 2014; 36 (4): C335-C352

View details for DOI 10.1137/130945569

View details for Web of Science ID 000344743800038
SYNCHROSQUEEZED CURVELET TRANSFORM FOR TWO-DIMENSIONAL MODE DECOMPOSITION SIAM JOURNAL ON MATHEMATICAL ANALYSIS Yang, H., Ying, L. 2014; 46 (3): 2052-2083

View details for DOI 10.1137/130939912

View details for Web of Science ID 000338830800015
A fast butterfly algorithm for generalized Radon transforms GEOPHYSICS Hu, J., Fomel, S., Demanet, L., Ying, L. 2013; 78 (4): T141-T151

View details for DOI 10.1190/GEO2012-0240.1

View details for Web of Science ID 000322716500051
Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition SIAM JOURNAL ON IMAGING SCIENCES Yang, H., Ying, L. 2013; 6 (4): 1979-2009

View details for DOI 10.1137/120891113

View details for Web of Science ID 000328890700006
Wave atoms and time upscaling of wave equations NUMERISCHE MATHEMATIK Demanet, L., Ying, L. 2009; 113 (1): 1-71

View details for DOI 10.1007/s00211-009-0226-6

View details for Web of Science ID 000267108700001
A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS MULTISCALE MODELING & SIMULATION Candes, E., Demanet, L., Ying, L. 2009; 7 (4): 1727-1750

View details for DOI 10.1137/080734339

View details for Web of Science ID 000270192800009
Wave atoms and sparsity of oscillatory patterns APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS Demanet, L., Ying, L. 2007; 23 (3): 368-387

View details for DOI 10.1016/j.acha.2007.03.003

View details for Web of Science ID 000251353200005
Curvelets and wave atoms for mirror-extended images Conference on Wavelets XII Demanet, L., Ying, L. SPIE-INT SOC OPTICAL ENGINEERING. 2007

View details for DOI 10.1117/12.733257

View details for Web of Science ID 000252227400018
Fast computation of Fourier integral operators SIAM JOURNAL ON SCIENTIFIC COMPUTING Candes, E., Demanet, L., Ying, L. 2007; 29 (6): 2464-2493

View details for Web of Science ID 000251175000011
Fast discrete curvelet transforms MULTISCALE MODELING & SIMULATION Candes, E., Demanet, L., Donoho, D., Ying, L. 2006; 5 (3): 861-899

View details for DOI 10.1137/05064182X

View details for Web of Science ID 000242572200007

Lexing Ying

Professor of Mathematics

Academic Appointments

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Additional Info

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2023-24 Courses

2022-23 Courses

2021-22 Courses

2020-21 Courses

Stanford Advisees

All Publications

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