Academic Appointments
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Professor, Mathematics
Honors & Awards
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SIAM Fellow, SIAM (2024)
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Invited lecture, The International Congress of Mathematicians (2022)
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Morningside Silver Medal of Applied Mathematics, ICCM (2016)
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James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, SIAM (2013)
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Feng Kang Prize of Scientific Computing, Chinese Academy of Sciences (2011)
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CAREER Award, National Science Foundation (2009)
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Alfred P. Sloan Research Fellowship, Sloan Foundation (2007)
2024-25 Courses
- Topics in Applied Math: Quantum Algorithms for Scientific Computation
MATH 275A (Aut) - Computational Methods of Applied Mathematics
CME 306, MATH 220B (Win) - Introduction to scientific computing with machine learning applications
CME 108 (Aut) -
Independent Studies (5)
- Advanced Reading and Research
MATH 360 (Aut, Win, Spr, Sum) - Curricular Practical Training
CME 390 (Aut, Win, Spr, Sum) - Master's Research
CME 291 (Aut, Win, Spr, Sum) - Ph.D. Research
CME 400 (Aut, Win, Spr, Sum) - Ph.D. Research Rotation
CME 391 (Aut, Win, Spr, Sum)
- Advanced Reading and Research
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Prior Year Courses
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)
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)
- Computational Methods of Applied Mathematics
Stanford Advisees
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Doctoral Dissertation Reader (AC)
Daniel Paul Kunin -
Doctoral Dissertation Advisor (AC)
Haoxuan Chen, Rajat Dwaraknath, Yinuo Ren, Xun Tang -
Doctoral Dissertation Co-Advisor (AC)
Ya-Chi Chu, Shaghayegh Fazliani, Milo Marsden
All Publications
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Meta-learning pseudo-differential operators with deep neural networks
JOURNAL OF COMPUTATIONAL PHYSICS
2020; 408
View details for DOI 10.1016/j.jcp.2020.109309
View details for Web of Science ID 000521731200026
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Solving electrical impedance tomography with deep learning
JOURNAL OF COMPUTATIONAL PHYSICS
2020; 404
View details for DOI 10.1016/j.jcp.2019.109119
View details for Web of Science ID 000507854200027
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Hessian transport gradient flows
RESEARCH IN THE MATHEMATICAL SCIENCES
2019; 6 (4)
View details for DOI 10.1007/s40687-019-0198-9
View details for Web of Science ID 000509100300001
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BCR-Net: A neural network based on the nonstandard wavelet form
JOURNAL OF COMPUTATIONAL PHYSICS
2019; 384: 1–15
View details for DOI 10.1016/j.jcp.2019.02.002
View details for Web of Science ID 000460888400001
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A multiscale neural network based on hierarchical nested bases
RESEARCH IN THE MATHEMATICAL SCIENCES
2019; 6 (2)
View details for DOI 10.1007/s40687-019-0183-3
View details for Web of Science ID 000464654500001
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Simple, direct and efficient multi-way spectral clustering
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
2019; 8 (1): 181–203
View details for DOI 10.1093/imaiai/iay008
View details for Web of Science ID 000469774500006
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Fast algorithms for integral formulations of steady-state radiative transfer equation
JOURNAL OF COMPUTATIONAL PHYSICS
2019; 380: 191–211
View details for DOI 10.1016/j.jcp.2018.12.014
View details for Web of Science ID 000458145900009
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CONVEX RELAXATION APPROACHES FOR STRICTLY CORRELATED DENSITY FUNCTIONAL THEORY
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2019; 41 (4): B773–B795
View details for DOI 10.1137/18M1207478
View details for Web of Science ID 000483924100032
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Numerical methods for Kohn-Sham density functional theory
ACTA NUMERICA
2019; 28: 405–539
View details for DOI 10.1017/S0962492919000047
View details for Web of Science ID 000491992100004
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SWITCHNET: A NEURAL NETWORK MODEL FOR FORWARD AND INVERSE SCATTERING PROBLEMS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2019; 41 (5): A3182–A3201
View details for DOI 10.1137/18M1222399
View details for Web of Science ID 000493897100019
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Sparsifying preconditioner for the time-harmonic Maxwell's equations
JOURNAL OF COMPUTATIONAL PHYSICS
2019; 376: 913–23
View details for DOI 10.1016/j.jcp.2018.10.004
View details for Web of Science ID 000450337400042
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SPARSIFY AND SWEEP: AN EFFICIENT PRECONDITIONER FOR THE LIPPMANN- SCHWINGER EQUATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2018; 40 (2): B379–B404
View details for DOI 10.1137/17M1132057
View details for Web of Science ID 000431100400028
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AN ENTROPIC FOURIER METHOD FOR THE BOLTZMANN EQUATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2018; 40 (5): A2858–A2882
View details for DOI 10.1137/17M1127041
View details for Web of Science ID 000448803100003
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SCDM-k: Localized orbitals for solids via selected columns of the density matrix
JOURNAL OF COMPUTATIONAL PHYSICS
2017; 334: 1-15
View details for DOI 10.1016/j.jcp.2016.12.053
View details for Web of Science ID 000395210500001
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ADAPTIVELY COMPRESSED POLARIZABILITY OPERATOR FOR ACCELERATING LARGE SCALE AB INITIO PHONON CALCULATIONS
MULTISCALE MODELING & SIMULATION
2017; 15 (1): 29-55
View details for DOI 10.1137/16M1077325
View details for Web of Science ID 000398614800002
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COMPUTING LOCALIZED REPRESENTATIONS OF THE KOHN-SHAM SUBSPACE VIA RANDOMIZATION AND REFINEMENT
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2017; 39 (6): B1178–B1198
View details for DOI 10.1137/16M1098589
View details for Web of Science ID 000418659900007
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TENSOR NETWORK SKELETONIZATION
MULTISCALE MODELING & SIMULATION
2017; 15 (4): 1423–47
View details for DOI 10.1137/16M1082676
View details for Web of Science ID 000418691000005
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Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
2016; 69 (8): 1415-1451
View details for DOI 10.1002/cpa.21582
View details for Web of Science ID 000379919000001
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Hierarchical Interpolative Factorization for Elliptic Operators: Integral Equations
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
2016; 69 (7): 1314-1353
View details for DOI 10.1002/cpa.21577
View details for Web of Science ID 000379917800003
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Sparsifying preconditioner for soliton calculations
JOURNAL OF COMPUTATIONAL PHYSICS
2016; 315: 458-466
View details for DOI 10.1016/j.jcp.2016.03.061
View details for Web of Science ID 000374832700025
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RECURSIVE SWEEPING PRECONDITIONER FOR THE THREE-DIMENSIONAL HELMHOLTZ EQUATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2016; 38 (2): A814-A832
View details for DOI 10.1137/15M1010154
View details for Web of Science ID 000375484800009
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A TECHNIQUE FOR UPDATING HIERARCHICAL SKELETONIZATION-BASED FACTORIZATIONS OF INTEGRAL OPERATORS
MULTISCALE MODELING & SIMULATION
2016; 14 (1): 42-64
View details for DOI 10.1137/15M1024500
View details for Web of Science ID 000373366500002
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ADDITIVE SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION
MULTISCALE MODELING & SIMULATION
2016; 14 (2): 799-822
View details for DOI 10.1137/15M1017144
View details for Web of Science ID 000379356600008
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Low-rank one-step wave extrapolation for reverse time migration
GEOPHYSICS
2016; 81 (1): S39-S54
View details for DOI 10.1190/GEO2015-0183.1
View details for Web of Science ID 000377880100046
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Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
JOURNAL OF COMPUTATIONAL PHYSICS
2015; 302: 329-335
View details for DOI 10.1016/j.jcp.2015.09.014
View details for Web of Science ID 000364256100018
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Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms Application of time-frequency analysis to art investigation
IEEE SIGNAL PROCESSING MAGAZINE
2015; 32 (4): 55-63
View details for DOI 10.1109/MSP.2015.2406882
View details for Web of Science ID 000356539400009
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Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix.
Journal of chemical theory and computation
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
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Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
2015; 11 (4): 1463-1469
View details for DOI 10.1021/ct500985f
View details for Web of Science ID 000353176500013
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A fast algorithm for 3D azimuthally anisotropic velocity scan
GEOPHYSICAL PROSPECTING
2015; 63 (2): 368-377
View details for DOI 10.1111/1365-2478.12180
View details for Web of Science ID 000349974600007
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A FAST ALGORITHM FOR THE ENERGY SPACE BOSON BOLTZMANN COLLISION OPERATOR
MATHEMATICS OF COMPUTATION
2015; 84 (291): 271-288
View details for Web of Science ID 000351441400010
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DIRECTIONAL PRECONDITIONER FOR 2D HIGH FREQUENCY OBSTACLE SCATTERING
MULTISCALE MODELING & SIMULATION
2015; 13 (3): 829-846
View details for DOI 10.1137/140985135
View details for Web of Science ID 000362421000005
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CRYSTAL IMAGE ANALYSIS USING 2D SYNCHROSQUEEZED TRANSFORMS
MULTISCALE MODELING & SIMULATION
2015; 13 (4): 1542-1572
View details for DOI 10.1137/140955872
View details for Web of Science ID 000367090400017
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SPARSIFYING PRECONDITIONER FOR THE LIPPMANN-SCHWINGER EQUATION
MULTISCALE MODELING & SIMULATION
2015; 13 (2): 644-660
View details for DOI 10.1137/140985147
View details for Web of Science ID 000357405000010
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BUTTERFLY FACTORIZATION
MULTISCALE MODELING & SIMULATION
2015; 13 (2): 714-732
View details for DOI 10.1137/15M1007173
View details for Web of Science ID 000357405000013
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FAST DIRECTIONAL COMPUTATION OF HIGH FREQUENCY BOUNDARY INTEGRALS VIA LOCAL FFTs
MULTISCALE MODELING & SIMULATION
2015; 13 (1): 423-439
View details for Web of Science ID 000352234400015
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SPARSIFYING PRECONDITIONER FOR PSEUDOSPECTRAL APPROXIMATIONS OF INDEFINITE SYSTEMS ON PERIODIC STRUCTURES
MULTISCALE MODELING & SIMULATION
2015; 13 (2): 459-471
View details for DOI 10.1137/140985159
View details for Web of Science ID 000357405000001
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A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS
MULTISCALE MODELING & SIMULATION
2015; 13 (2): 614-631
View details for DOI 10.1137/140997658
View details for Web of Science ID 000357405000008
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SWEEPING PRECONDITIONERS FOR ELASTIC WAVE PROPAGATION WITH SPECTRAL ELEMENT METHODS
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
2014; 48 (2): 433-447
View details for DOI 10.1051/m2an/2013114
View details for Web of Science ID 000331943800007
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A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
JOURNAL OF COMPUTATIONAL PHYSICS
2014; 258: 227-245
View details for DOI 10.1016/j.jcp.2013.10.030
View details for Web of Science ID 000329118500012
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A PARALLEL BUTTERFLY ALGORITHM
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (1): C49-C65
View details for DOI 10.1137/130921544
View details for Web of Science ID 000333415500023
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POLE EXPANSION FOR SOLVING A TYPE OF PARAMETRIZED LINEAR SYSTEMS IN ELECTRONIC STRUCTURE CALCULATIONS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (6): A2929-A2951
View details for DOI 10.1137/130944825
View details for Web of Science ID 000346838800019
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A PARALLEL DIRECTIONAL FAST MULTIPOLE METHOD
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (4): C335-C352
View details for DOI 10.1137/130945569
View details for Web of Science ID 000344743800038
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SYNCHROSQUEEZED CURVELET TRANSFORM FOR TWO-DIMENSIONAL MODE DECOMPOSITION
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
2014; 46 (3): 2052-2083
View details for DOI 10.1137/130939912
View details for Web of Science ID 000338830800015
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A fast butterfly algorithm for generalized Radon transforms
GEOPHYSICS
2013; 78 (4): T141-T151
View details for DOI 10.1190/GEO2012-0240.1
View details for Web of Science ID 000322716500051
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Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition
SIAM JOURNAL ON IMAGING SCIENCES
2013; 6 (4): 1979-2009
View details for DOI 10.1137/120891113
View details for Web of Science ID 000328890700006
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Wave atoms and time upscaling of wave equations
NUMERISCHE MATHEMATIK
2009; 113 (1): 1-71
View details for DOI 10.1007/s00211-009-0226-6
View details for Web of Science ID 000267108700001
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A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
MULTISCALE MODELING & SIMULATION
2009; 7 (4): 1727-1750
View details for DOI 10.1137/080734339
View details for Web of Science ID 000270192800009
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Wave atoms and sparsity of oscillatory patterns
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
2007; 23 (3): 368-387
View details for DOI 10.1016/j.acha.2007.03.003
View details for Web of Science ID 000251353200005
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Curvelets and wave atoms for mirror-extended images
Conference on Wavelets XII
SPIE-INT SOC OPTICAL ENGINEERING. 2007
View details for DOI 10.1117/12.733257
View details for Web of Science ID 000252227400018
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Fast computation of Fourier integral operators
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2007; 29 (6): 2464-2493
View details for Web of Science ID 000251175000011
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Fast discrete curvelet transforms
MULTISCALE MODELING & SIMULATION
2006; 5 (3): 861-899
View details for DOI 10.1137/05064182X
View details for Web of Science ID 000242572200007