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Yu Guang Wang
Scientist	Email:	yuguang.wang@mis.mpg.de yuguang.wang@unsw.edu.au
Max Planck Institute for Mathematics in the Sciences & University of New South Wales	Mail:	Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig Germany

Introduction

I am a scientist (postdoc) at Max Planck Institute for Mathematics in Sciences, hosted by Prof Guido Montúfar. I am also an adjunct associate lecturer at UNSW Sydney. My research interests lie in computational mathematics, statistics, machine learning, and data science. In particular, I am working on deep learning, graph neural networks, applied harmonic analysis, Bayesian inference, information geometry, random fields, numerical analysis, and applications to healthcare, biomedical technology and cosmology. I obtained my PhD in applied mathematics from University of New South Wales under supervision of Prof Ian Sloan and Rob Womersley. I have been a semester-long visitor of IPAM, UCLA (2019) and ICERM, Brown University (2018).

Current Research Interests

• Data Science and Machine Learning: Graph Neural Networks, Deep Learning, Information Geometry, Optimization Algorithms, Distributed Learning, Generative Models, Topological Data Analysis, Expressive Power of Deep Neural Networks
• Applied Math and Statistics: Applied Harmonic Analysis, Signal Processing, Bayesian Statistics, Computational Geometry, SDEs
• Applications: AI Diagnostics, Personalised Medicine, Cosmic Microwave Background (CMB)

Publications

    List of publications can be found at my Google Scholar.

Book Chapter

• Analysis of Framelet Transforms on Simplex.
  Y. G. Wang, H. Zhu.
  Contemporary Computational Mathematics: a Celebration for the 80th Birthday of Ian Sloan. Editors: Josef Dick, Frances Y. Kuo, Henryk Wozniakowski, Publisher: Springer, 2018.

Technical Report

• White Paper: Geometry and Learning from Data in 3D and Beyond.
  P. Kr. Banerjee, Y. G. Wang et al.
  Technical Report, IPAM Long Program, Spring 2019.

Papers

Submitted

• How Framelets Enhance Graph Neural Networks.
  X. Zheng, B. Zhou, J. Gao, Y. G. Wang, P. Lio, M. Li, G. Montufar.
  


• Decimated Framelet System on Graphs and Fast G-Framelet Transforms.
  X. Zheng, B. Zhou, Y. G. Wang, X. Zhuang.
  Codes


• Numerical Computation of Triangular Complex Spherical Designs with Small Mesh Ratio.
  Y. G. Wang, R. S. Womersley, H.-T. Wu, W.-S. Yu.
  


• MathNet: Haar-Like Wavelet Multiresolution-Analysis for Graph Representation and Learning.
  X. Zheng, B. Zhou, M. Li, Y. G. Wang, J. Gao.
  


• Power-law Scaling of Brain Wave Activity Associated with Mental Fatigue.
  V. V. Anh, H. T. Nguyen, A. Craig, Y. Tran, Y. G. Wang.
  


• Distributed Learning via Filtered Hyperinterpolation on Manifolds.
  G. Montufar, Y. G. Wang.
  


• On the Approximation Lower Bound for Neural Nets with Random Weights.
  S. Sonoda, M. Li, F. Cao, C. Huang, Y. G. Wang.
  


• FaVeST: Fast Vector Spherical Harmonic Transforms.
  M. Li, Q. T. Le Gia, Y. G. Wang.
  


• Fast Tensor Needlet Transforms for Tangent Vector Fields on the Sphere.
  M. Li, P. Broadbridge, A. Olenko, Y. G. Wang.
  



2015–2021

• Improve Concentration of Frequency and Time by Novel Complex Spherical Designs.
  M. Sourisseau, Y. G. Wang, R. S. Womersley, H.-T. Wu, W.-H. Yu.
  Applied and Computational Harmonic Analysis, 2021. Codes


• A New Probe of Gaussianity and Isotropy with Application to Cosmic Microwave Background Maps.
  J. Hamann, Q. T. Le Gia, I. H. Sloan, Y. G. Wang, R. S. Womersley.
  International Journal of Modern Physics C, 2021. Codes
  


• Can Neural Networks Learning persistent homology features?
  G. Montufar, N. Otter, Y. G. Wang.
  NeurIPS Workshop on TDA and Beyond, 2020.


• Distributed Filtered Hyperinterpolation For Noisy Data on the Sphere.
  S.-B. Lin, Y. G. Wang, D.-X. Zhou.
  SIAM Journal on Numerical Analysis, 2020.


• Path Integral Based Convolution and Pooling for Graph Neural Networks.
  Z. Ma, J. Xuan, Y. G. Wang, M. Li, P. Lio.
  NeurIPS, 2020. Codes


• Haar Graph Pooling.
  Y. G. Wang, M. Li, Z. Ma, G. Montufar, X. Zhuang, Y. Fan.
  ICML, 2020. Codes


• Fast Haar Transforms for Graph Neural Networks.
  M. Li, Z. Ma, Y. G. Wang, X. Zhuang.
  Neural Networks, 2020.


• Deep Learning Based Unsupervised and Semi-supervised Classification for Keratoconus.
  N. Hallett, K. Yi, J. Dick, C. Hodge, G. Sutton, Y. G. Wang, J. You.
  IJCNN, 2020.


• CosmoVAE: Variational Autoencoder for CMB Image Inpainting.
  K. Yi, Y. Guo, Y. Fan, J. Hamann, Y. G. Wang.
  IJCNN, 2020.


• Tight Framelets and Fast Framelet Filter Bank Transforms on Manifolds.
  Y. G. Wang, X. Zhuang.
  Applied and Computational Harmonic Analysis, 48(1): 64–95, 2020.


• Isotropic Sparse Regularization for Spherical Harmonic Representations of Random Fields on the Sphere.
  Q. T. Le Gia, I. H. Sloan, R. S. Womersley, Y. G. Wang.
  Applied and Computational Harmonic Analysis, 49(1): 257–278, 2020.


• Tight framelets on graphs for multiscale data analysis.
  Y. G. Wang, X. Zhuang.
  Wavelets and Sparsity XVIII, SPIE Proc., pp. 11 138–11, 2019.


• PAN: Path Integral Based Convolution for Deep Graph Neural Networks.
  Z. Ma, M. Li, Y. G. Wang.
  ICML Workshop on Learning and Reasoning with Graph-Structured Representations, 2019. Codes


• On Approximation of Fractional Stochastic Partical Differential Equations on the Sphere.
  V. V. Anh, P. Broadbridge, A. Olenko, Y. G. Wang.
  Stochastic Environmental Research and Risk Assessment, 2018.


• Riemann Localisation on the Sphere.
  Y. G. Wang, I. H. Sloan, R. S. Womersley.
  Journal of Fourier Analysis and Applications, 24(1): 141–183, 2018.


• Random Point Sets on the Sphere — Hole Radii, Covering, and Separation.
  J. S. Brauchart, E. B. Saff, I. H. Sloan, Y. G. Wang, R. S. Womersley.
  Experimental Mathematics, 27(1): 62–81, 2018.


• Fully Discrete Needlet Approximation on the Sphere.
  Y. G. Wang, Quoc T. Le Gia, I. H. Sloan, R. S. Womersley.
  Applied and Computational Harmonic Analysis, 43: 292–316, 2017. Codes


• Needlet Approximation for Isotropic Random Fields on the Sphere.
  Y. G. Wang, Quoc T. Le Gia, I. H. Sloan, R. S. Womersley.
  Journal of Approximation Theory, 216: 86–116, 2017.


• Filtered Polynomial Approximation on the Sphere.
  Y. G. Wang.
  Bulletin of the Australian Mathematical Society, 93(01): 162–163, 2016.


• An Iterative Learning Algorithm for Feedforward Neural Networks with Random Weights.
  F. Cao, D. Wang, H. Zhu, Y. G. Wang.
  Information Sciences, 328: 546–557, 2016.


• Covering of Spheres by Spherical Caps and Worst-case Error for Equal Weight Cubature in Sobolev Spaces.
  J. S. Brauchart, J. Dick, E. B. Saff, I. H. Sloan, YG. Wang, R. S. Womersley.
  Journal of Mathematical Analysis and Applications, 431(2):782–811, 2015.



Before 2015

• Approximation by Semigroup of Spherical Operators.
  Y. G. Wang, F. Cao.
  Frontiers of Mathematics in China, 9(2):387–416, 2014.


• A Modified Extreme Learning Machine with Sigmoidal Activation Functions.
  Z. Chen, H. Zhu, Y. G. Wang.
  Neural Computing and Applications, 22(3-4):541–550, 2013. Codes


• Optimization Approximation Solution for Regression Problem Based on Extreme Learning Machine.
  Y. Yuan, Y. G. Wang, F. Cao.
  Neurocomputing, 74(16):2475–2482, 2011. Codes


• A Study on Effectiveness of Extreme Learning Machine.
  Y. G. Wang, F. Cao, Y. Yuan.
  Neurocomputing, 74(16):2483–2490, 2011. Codes


• Approximation by Boolean Sums of Jackson Operators on the Sphere.
  Y. G. Wang, F. Cao.
  Journal of Computational Analysis and Applications, 13(5):830–842, 2011.


• The Direct and Converse Inequalities for Jackson-type Operators on Spherical Cap.
  Y. G. Wang, F. Cao.
  Journal of Inequalities and Applications, Art. ID 205298, 16 pages, 2009.

Recent and Upcoming Seminars

	•	Deep Learning Theory & Math Machine Learning Seminar, MPI MIS + UCLA, Virtual, Regular, 2021.
	•	Annual Meeting of Australian Mathematical Society (AustMS'20), University of New England, Virtual, 8 Dec - 10 Dec 2020.
	•	Thirty-fourth Conference on Neural Information Processing Systems (NeurIPS'20), Virtual, 6 Dec - 12 Dec 2020.
	•	AI Group Seminar, University of Cambridge, Virtual, 28 Oct 2020.
	•	IMA Workshop on Theory and Algorithms in Graph-based Learning, University of Minnesota, Virtual, 14 Sep - 18 Sep 2020.
	•	GAMM AG Workshop Computational and Mathematical Methods in Data Science, MPI MIS, Virtual, 10 Sep - 11 Sep 2020.
	•	Thirty-seventh International Conference on Machine Learning (ICML'20), Virtual, 12 Jul - 18 Jul 2020.

Service

I am a Guest Editor for Special Issue Deep Neural Networks for Graphs: Theory, Models, Algorithms and Applications in IEEE Transactions on Neural Networks and Learning Systems (Top AI Journal). Call for Papers!

I am a review Editor for the journal Frontiers in Applied Mathematics and Statistics.

I am a reviewer for ICML'20 (Top Reviewer), ICML'21, NeurIPS'20, ICLR'21, IJCAI'21.

I am an organiser for Collaborate@ICERM on Geometry of Data and Networks, 2019 joint with Joan Bruna (NYU), Zheng Ma (Princeton), Guido Montúfar (UCLA), Nina Otter (UCLA).

I am an organiser for Minisymposium on Harmonic Analysis for Graph Signal Processing and Deep Learning Applications in SIAM Conference on Mathematics of Data Science 2020 (MDS20) joint with Xiaosheng Zhuang (CityU HK).

Teaching and Supervision

I was a class tutor in UNSW for following courses.

		Semester 3 2019, MATH3101/5305 Computational Mathematics (Numerical Methods for PDEs)
		Semester 2 2018, MATH2089 Numerical Methods and Statistics
		Semester 1 2015, MATH1131 Mathematics 1A
		Semester 2 2014, MATH1231 Mathematics 1B, MATH1241 Higher Mathematics 1B, MATH2019 Engineering Mathematics 2E

I am supervising four PhD students:

		Kai Yi, UNSW Statistics and Data Science, research on deep Bayesian learning, graph neural networks, since 2019 (chief supervisor, joint with A/Prof Yanan Fan, Dr Jan Hamann)
		Xuebin Zheng, University of Sydney Business Analytics, research on graph neural networks, since 2018 (co-supervisor, with Prof Junbin Gao)
		Bingxin Zhou, University of Sydney Business Analytics, research on graph neural networks, manifold learning, since 2018 (co-supervisor, with Prof Junbin Gao).
		Nicole Hallet, University of Sydney Medicine, research on cornea AI, since 2018 (co-supervisor, with Prof Gerard Sutton, Dr Jingjing You).

I have co-supervised two masters students in Statistics and Data Science at UNSW, 2018–2019:

		Yi Guo, thesis title: Cosmo-Encoder: A Bayesian deep learning approach for cosmic microwave background inpainting
		Kai Yi, thesis title: Variational autoencoder for cosmic microwave background image inpainting.

Copyright @ 2020 Yu Guang Wang

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