Research Interests:
Grants:
Mathematical Analysis and Computational Challenges in Data Science. Role: single PI. Amount: SGD 120,000. Duration: 2017-2020.
AMS Simons Travel Award, USD 4,000. Duration: 2015-2017.
Ph.D. Dissertation:
Journal Publications:
[34] K. R. Phillips, T. Yang, C. T. Zhang, T. Kay, C. Gao, S. Brandt, L. Liu, H. Yang, Y. Li, J. Aizenberg, L. Li. Fabrication of Photonic Microbricks via Crack Engineering of Colloidal Crystals. Preprint.
[33] Z. Shen, H. Yang, S. Zhang. Nonlinear Approximation via Compositions. Submitted.
[32] Y. Liu, H. Yang. A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electro- magnetic Scattering Problems Involving Open Surfaces. Submitted.
[31] J. Bremer, Q. Pang, H. Yang, Fast Algorithms for Multi-dimensional Jacobi Polynomial Transforms. Submitted.
[30] S. Liang, Y. Kwoo, H. Yang, Drop-Activation: Implicit Parameter Reduction and Harmonic Regularization. Submitted.
[29] T. Zhang, L. Li, H. Yang, 3D Crystal Image Analysis based on Fast Synchrosqueezed Transforms. Submitted.
[28] Q. Pang, K. Ho, H. Yang, Interpolative Decomposition Butterfly Factorization. Submitted.
[27] J. Xu, Y. Li, D. Dunson, I. Daubechies, H. Yang, Non-Oscillatory Pattern Learning for Non-Stationary Signals. Submitted.
[26] J. Bremer, H. Yang, Fast Algorithms for Jacobi Expansions via Nonoscillatory Phase Functions. To appear, IMA Journal of Numerical Analysis.
[25] H. Yang, A Unified Framework for Oscillatory Integral Transform: When to use NUFFT or Butterfly Factorization? To appear, Journal of Computational Physics.
[24] G. Tang, H. Yang, A Fast Algorithm for Multiresolution Mode Decomposition. Submitted.
[23] H. Yang, Multiresolution Mode Decomposition for Adaptive Time Series Analysis. Submitted.
[22] L. Li, H. Yang, K. Pillips, J. Zhong, J. Lu, and J. Aizenberg, Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals. Submitted.
[21] J. Harlim and H. Yang, Diffusion Forecasting Model with Basis Functions from QR Decomposition. Journal of Nonlinear Science, 2017.
[20] V. W-z Yu, F. Corsetti, A. García, W. P Huhn, M. Jacquelin, W. Jia, B. Lange, L. Lin, J. Lu, W. Mi, A. Seifitokaldani, Á. Vázquez-Mayagoitia, C. Yang, H. Yang, V. Blum, ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers. Compute Physics Communications, Volume 222, January 2018, Pages 267-285.
[19] H. Yang and J. Lu, Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms. To appear, SIAM Journal on Imaging Science.
[18] Y. Li, and H. Yang, Interior Eigensolver for Sparse Hermitian Definite Matrices Based on Zolotarevs Functions. Submitted.
[17] J. Lu, and H. Yang, A Cubic Scaling Algorithm to Calculate Excited States Based on Particle-Particle Random Phase Approximation, Journal of Computational Physics, Volume 340, 1 July 2017, Pages 297-308.
[16] J. Xu, H. Yang, and I. Daubechies, Recursive Diffeomorphism-Based Regression for Shape Functions. SIAM Journal on Mathematical Analysis, 50(1), 5-32, 2018.
[15] Y. Li, and H. Yang, Interpolative Butterfly Factorization, SIAM Journal on Scientific Computing, 2017.
[14] J. Lu, and H. Yang, Preconditioning Orbital Minimization Method for Planewave Discretization, SIAM Multiscale Modeling and Simulation, 2016.
[13] B. Cornelis, H. Yang, A. Goodfriend, N. Ocon, J. Lu, and I. Daubechies, Removal of Canvas Patterns in Digital Acquisitions of Paintings, IEEE Transactions on Image Processing, 2016.
[12] Y. Li, H. Yang, and L. Ying, Multidimensional Butterfly Factorization, Applied and Computational Harmonic Analysis, 2017.
[11] Y. Li, H. Yang, E. Martin, K. Ho and L. Ying, Butterfly Factorization, SIAM Multiscale Modeling and Simulation, 2015.
[10] J. Lu, B. Wirth, H. Yang, Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis , Journal of the Mechanics and Physics of Solids, 2016.
[9] Y. Li, H. Yang and L. Ying, A Multiscale Butterfly Aglorithm for Multidimensional Fourier Integral Operators. , SIAM Multiscale Modeling and Simulation, 2015.
[8] H. Yang, Statistical Analysis of Synchrosqueezed Transforms. , Applied and Computational Harmonic Analysis, 2017. Codes.
[7] H. Yang, J. Lu and L. Ying, Crystal Image Analysis Using 2D Synchrosqueezed Transforms. , SIAM Multiscale Modeling and Simulation, 2015.
[6] H. Yang, J. Lu, W. P. Brown, I. Daubechies, and L. Ying, Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms. , IEEE Signal Processing Magazine, 2015.
[5] H. Yang, Synchrosqueezed Wave Packet Transforms and Diffeomorphism Based Spectral Analysis for 1D General Mode Decompositions. Applied and Computational Harmonic Analysis, 2015.
[4] H. Yang and L. Ying, Synchrosqueezed Curvelet Transform for 2D. Mode Decomposition, SIAM Journal of Mathematical Analysis, 2014.
[3] H. Yang and L. Ying, Synchrosqueezed Wave Packet Transform for 2D. Mode Decomposition, SIAM Journal on Imaging Science, 2013.
[2] H. Yang and L. Ying, A Fast Algorithm for Multilinear Operators, Applied and Computational Harmonic Analysis, 2012.
[1]
Z. Xu, X. Cheng and H. Yang,
Treecode-based generalized Born method,
J. Chem. Phys., 2011.
Conference Proceedings:
[1] William Huhn, Alberto Garcia, Luigi Genovese, Ville Havu, Mathias Jacquelin, Weile Jia, Murat Keceli, Raul Laasner, Yingzhou Li, Lin Lin, Jianfeng Lu, Stephan Mohr, Nkwe Monama, Happy Sithole, Alvaro Vazquez-Mayagoitia, Chao Yang, Haizhao Yang, Victor Yu, Volker Blum. Unified Access To Kohn-Sham DFT Solvers for Different Scales and HPC: The ELSI Project. Bulletin of the American Physical Society, 2018.
Conferences and Workshops:
O(N log N) matvec and preconditioners for highly oscillatory kernels, International Council for Industrial and Applied Mathematics (ICIAM), Spain, July, 2019
Fast Algorithms for Calculating Excited States in PP-RPA, International Council for Industrial and Applied Mathematics (ICIAM), Spain, July, 2019
Approximation Theory of Deep Learning in Scientific Computing, Workshop on Machine Learning Techniques in Scientific Computing. Wuhan University, China, June, 2019
O(N log N ) algorithms for matrix multiplications from highly oscillatory phenomena, SIAM Conference on Computational Science and Engineering (CSE), Washington, US, February, 2019
Optimal Approximation Theory of Parallel Deep Learning, International Congress of Chinese Mathematicians - Consortium on Computational and Applied Mathematics (ICCM-CAM), Nanjing, China, December, 2018
Fast eigenvalue solvers for pp-RPA, ELSI Conference: Solving or Circumventing Eigenvalue Problems in Electronic Structure Theory, The Molecular Sciences Software Institute-Blacksburg, Virginia, August 15-17, 2018
Fast eigenvalue solvers for pp-RPA, SIAM Conference on Applied Linear Algebra, Hong Kong, 2018
Automatic information learning for atomistic structure, SIAM Conference on Mathematical Aspects of Materials Science, Portland, US, 2018
The separation of signal components: geometric interpretation and random dynamics, SIAM Annual Meeting, Portland, US, 2018
On the Convergence of Recursive Schemes for Wave Shape Functions, SIAM Annual Meeting, 2017
Recursive schemes for shape functions in the mode decomposition problem, The First International Conference on Mathematics of Data Science (MathDS), Hong Kong, China, March, 2017
Preconditioning orbital minimization method for planewave discretization, 2016 Workshop on Optimization and Eigenvalue Computation, Peking University, Beijing, China.
Butterfly Factorization for a Class of Transforms in Harmonic Analysis, SIAM Annual Meeting, 2016
Canvas Texture Analysis for Art Investigation, SIAM Conference on Imaging Science, 2016
Butterfly factorization, February Fourier Talks 2016, University of Maryland, College Park, Maryland, USA
Variational Models for Crystal Image Analysis, SIAM Analysis of Partial Differential Equations, 2015
Butterfly Factorization, SIAM Applied Linear Algebra, 2015
Synchrosqueezed Transforms and Their Application in Seismic Data Analysis, ICIAM, 2015
Synchrosqueezed Transform and Variational Method for Crystal Image Analysis, ICIAM, 2015
Synchrosqueezed Transforms in Seismic Data/Image Analysis, The First International Workshop on Mathematical Geophysics at Harbin Institute of Technology, China, 2015
Robustness Analysis of Synchrosqueezed Transforms, SEG Annual Meeting Post Convention Workshop, 2014
Synchrosqueezed Wave Packet Transforms and Diffeomorphism Based Spectral Analysis for 1D General Mode Decompositions, SIAM Annual Meeting 2014
Synchrosqueezed Curvelet Transform for 2D mode decomposition, SIAM Conference on Imaging Science 2014
Synchrosqueezed Curvelet Transform for 2D mode decomposition, TCCS, March, 2014
Synchrosqueezed Wave Packet Transform for 2D mode decomposition, SIAM Annual Meeting 2013
Adaptive Data Analysis and Sparsity, IPAM, UCLA, 2013
Synchrosqueezed Wave Packet Transform for 2D mode decomposition, 4th TCCS, October, 2012
Fast computation for multilinear operators, 2th TCCS, September, 2011
Seminars and visiting:
Approximation Theory and Regularization in Deep Learning, Applied Math and Analysis Seminar, Duke University, February, 2019.O(N log N) matvec and preconditioners for highly oscillatory kernels, Applied and Computational Mathe- matics Seminar, Department of Mathematics, National University of Singapore, February, 2019.
O(N log N) matvec and preconditioners for highly oscillatory kernels, Applied Math Colloquium, Department of Mathematics, Purdue University, January, 2019.
O(N log N ) algorithms for matrix multiplications from highly oscillatory phenomena, Applied Mathematics Seminar, School of Mathematics, Shanghai Jiao Tong University, December, 2018.
O(N log N ) algorithms for matrix multiplications from highly oscillatory phenomena, Applied Mathematics Colloquium, Department of Applied Physics and Applied Mathematics, Columbia University, October, 2018.
A Unified Framework for Oscillatory Integral Transform: When to use NUFFT or Butterfly Factorization?, Applied Math Colloquium, Department of Mathematics, Purdue University, February, 2018.
A Unified Framework for Oscillatory Integral Transform: When to use NUFFT or Butterfly Factorization?, Applied & Computational Math Seminar, Department of Mathematics, University of Wisconsin-Madison, February, 2018.
Spectrum Slicing for Sparse Hermitian Definite Matrices Based on Zolotarev's Functions, Department of Mathematics, Hong Kong Baptist University, March, 2017.
Scientific Computing in Imaging and Image Analysis at the Atomic Scale, Department of Mathematics, Lawrence Berkeley National Laboratory, March, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Department of Mathematics, Johns Hopkins University, February, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Department of Mathematics, National University of Singapore, February, 2017.
Data-Sparse Structures and their Applications in the Electronic Structure Calculation, CCMA Luncheon Seminar, Department of Mathematics, The Pennsylvania State University, February, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Computational and Applied Mathematics Colloquium, Department of Mathematics, The Pennsylvania State University, February, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Colloquium, Department of Mathematics, University of California, Davis, January, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Colloquium, Department of Mathematics, University of California, Irvine, January, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Department of Mathematics, Hong Kong University of Science and Technology, January, 2017.
Data-Driven Mathematical Analysis and Scientific Computing for Oscillatory Data, Computational and Applied Math Seminar, Department of Mathematics, University of California, San Diego, December, 2016.
A Cubic Scaling Algorithm to Calculate Excited States Based on PP-RPA, Research Colloquium, Department of Mathematics, Southern Methodist University, November, 2016.
Data-Driven fast algorithms in Applied Harmonic Analysis and Numerical Linear Algebra, Applied Math and Analysis Seminar, Duke University, October, 2016.
Variational Models for Crystal Image Analysis, Hong Kong University of Science and Technology, Hong Kong, China, 2016.7.
Preconditioning orbital minimization method for planewave discretization, Shanghai Jiao Tong University, Shanghai, China, 2016.6.
Butterfly algorithm and butterfly factorization,
Shanghai Jiao Tong University, Shanghai, China, 2016.6.
Butterfly algorithm and butterfly factorization,
Applied Mathematics Colloquium, University of North Carolina at Chapel Hill
,
2016.3
2D Synchrosqueezed Transforms with Applications in Geophysics and Materials Science,
Shanghai Jiao Tong University,
2014.4
Synchrosqueezed Analysis in Signal and Image Processing,
Duke University,
2013.12
Synchrosqueezed Wave
Packet Transfrom,
Jr. Numerical
Analysis Seminar,
UT Austin, 2012.10
Subspaces Detection,
Jr. Numerical Analysis Seminar, UT Austin, 2012.4Fast computation for multilinear operators, Jr. Numerical Analysis Seminar, UT Austin, 2011.10