Matthew J. Hirn

Matthew J. Hirn

Assistant Professor, Department of Computational Mathematics, Science and Engineering; Department of Mathematics
Room 2507F, Engineering Building
 428 S. Shaw Ln.
 (517) 432-0611
 mhirn@msu.edu

About Me

Education:

B.A., 2004, mathematics, Cornell University

Ph.D. 2009, mathematics, University of Maryland

 

Awards:

Alfred P. Sloan Research Fellow

DARPA Young Faculty Award

NSF DMS Grant #1620216

 

Bio:

Matthew Hirn is an Assistant Professor in the Department of Computational Mathematics, Science and Engineering and the Department of Mathematics at Michigan State University, where he has been a faculty member since 2015.

Hirn’s research interests are at the interface of harmonic analysis and machine learning. Broadly speaking, he develops mathematically provable machine learning algorithms to circumvent prohibitively costly computations in scientific computing, thereby opening new avenues for scientific breakthroughs. This work synthesizes modern developments in harmonic analysis with cutting edge research in statistics and computer science. Tools that uncover complex, multiscale patterns in high dimensional data are constructed by considering the underlying data geometries, invariants, hierarchies and statistics. Specific research thrusts include:

     •    Wavelet theory and deep learning (scattering transforms)

     •    Diffusion based manifold learning 

     •    Smooth (Whitney) extensions and interpolations of data

     •    Many body problems in quantum chemistry

     •    Analysis of bio-medical data 

Hirn received his B.A. in mathematics from Cornell University under the supervision of Robert Strichartz, and his Ph.D. in mathematics at the University of Maryland, College Park under the supervision of John Benedetto and Kasso Okoudjou. While at the University of Maryland, he was a member of the Norbert Weiner Center for Harmonic Analysis and Applications.

Before arriving at Michigan State, Hirn held postdoctoral appointments in the Department of Mathematics at Yale University, as part of Ronald Coifman’s research group, and in the Département d’Informatique at the École normale supérieure, as part of Stéphane Mallat’s research group. He also held a brief appointment as a visiting assistant professor at Cornell University, where he directed an NSF-funded Research Experience for Undergraduates program on High Dimensional Data Analysis.

Research Interests

•    Applied Harmonic Analysis

•    Manifold Learning

•    Smooth Extensions and Interpolations

•    Deep Learning

•    Applications: quantum chemistry, N-body problems, image analysis, hyperspectral image analysis, flow cytometry, dynamical systems, fluid mechanics

CEDAR Team: ComplEx Data Analysis Research
CEDAR Team: ComplEx Data Analysis Research

Scientific Leader: Dr. Matthew Hirn

The CEDAR team works at the interface of harmonic analysis and machine learning. We develop tools that uncover complex, multiscale patterns in high dimensional data by considering the underlying data geometries, invariants, hierarchies and statistics. Our focus is on rigorous mathematical theory coupled with state of the art numerical results in application specific domains. Research areas include:

  • Wavelet theory and deep learning (scattering transforms)
  • Diffusion based manifold learning 
  • Smooth (Whitney) extensions and interpolations of data
  • Many body problems in quantum chemistry
  • Analysis of bio-medical data 
Selected Publications
Time Coupled Diffusion Maps
June 15, 2017
Time Coupled Diffusion Maps

Cornell Universiry Library published a paper by faculty member Matthew J. Hirn on 15 August, 2016.

Link: https://arxiv.org/abs/1608.03628

Wavelet Scattering Regression of Quantum Chemical Energies
June 8, 2017
Wavelet Scattering Regression of Quantum Chemical Energies

Multiscale Modeling and Simulation has published the following paper by Matthew Hirn, Stephane Mallat, & Nicolas Poilvert for their work in Wavelet Scattering on 2 May 2017.

Link: http://epubs.siam.org/doi/abs/10.1137/16M1075454

Computing Minimal Interpolants in C^1,1(R^d)
April 12, 2017
Computing Minimal Interpolants in C^1,1(R^d)

Ariel Herbert-Voss, Matthew J. Hirn, & Frederick McCollum published a paper in Revista Mathematica Iberoamericana for their work on Computing Minimal Interpolants.

Link: http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=33&iss=1&rank=2

Software Projects
C-1-1-Interpolation
C-1-1-Interpolation

Dr. Matt Hirn - Python program that Computes the optimal C^{1,1}(R^d) interpolations in any dimension d.

ScatNet-QM-2D
ScatNet-QM-2D

Dr. Matt Hirn - Wavelet scattering regression of quantum chemical energies for planar molecules.

This software computes two-dimensional wavelet scattering transforms of planar molecules and corresponding molecular energy regressions, as described in the paper "Wavelet scattering regression of quantum chemical energies," (https://arxiv.org/abs/1605.04654) by Matthew Hirn, Stéphane Mallat, and Nicolas Poilvert.

Wavelet Scattering Regression of Quantum Chemical Energies
Wavelet Scattering Regression of Quantum Chemical Energies

Dr. Matt Hirn - Matlab implementations of the algorithms described in “Wavelet Scattering Regression of Quantum Chemical Energies” (pdfarXiv

Teaching

No courses for Fall 2017 or Spring 2018.

Click "Teaching" link to see past courses.