George Stepaniants
NSF Postdoctoral Fellow
Caltech Computing + Mathematical Sciences
About Me
I am an NSF MSPRF postdoctoral fellow at the California Institue of Technology in the Department of Computing and Mathematical Sciences working with Prof. Andrew Stuart.
I recieved my PhD from the Massachusetts Institute of Technology (MIT) in 2024 in the Department of Mathematics co-advised by Prof. Philippe Rigollet and Prof. Jörn Dunkel funded by the NSF GRFP and MIT Presidential Fellowship.
I was also part of the Interdisciplinary Doctoral Program in Statistics (IDPS) through the Institute for Data, Systems, and Society (IDSS).
Prior to MIT, I graduated in 2019 from the University of Washington (UW) with a Bachelors of Science in Mathematics and Computer Science where I performed research on network inference methods in the Department of Applied Mathematics under Prof. Nathan Kutz.
As an applied mathematician, I study how the partial, incomplete, and noisy data we collect from physical systems leads to degrees of freedom along which a physical model cannot be resolved. Across a wide range of problems concerning mechanics of materials, fluid flows, biophysical processes, and network dynamics, my goal is to develop mathematical theory and data-driven machine learning architectures that allow us to learn the maximal amount of information from such partially observed systems. My teaching philosophy is inspired by my research, showing students how to discover interesting mathematical ideas in field-specific literature, translate them into well-posed mathematical theories, and when possible, bring these theories to life as numerical algorithms.
Research Highlights
My research develops statistical and machine learning methods to model spatial and time varying processes from data; specifically in physical, biological and engineering problems where nonlocal effects are present. Examples include inference of dynamic networks, Green’s functions, autoregressive or memory kernel models, and fractional order equations. These methods are also applicable to partially observed systems, which often display nonlocal interactions in the observed coordinates as well as in time. I also explore how data and systems can be compared using statistical tools such as optimal transport.
Differential Equations
3 projects
Optimal Transport
2 projects
Neural Networks
1 project
Education
University of Washington,
Seattle
BSc (2015-2019)
Math and Computer Science Double Major
Massachusetts Institute
of Technology
PhD (2019-2024)
NSF GRFP Graduate Student in Mathematics and Statistics
California Institute
of Technology
Postdoc (2024-2027)
NSF MSPRF Postdoctoral Researcher
at Computing + Mathematical Sciences
News Highlights
NSF Mathematical Sciences Postdoctoral Research Fellow (MSPRF)
Sep 2024
IMS Lawrence D. Brown Ph.D. Student Award Recipient
Sep 2024
NSF Graduate Research Fellow (GRFP)
Sep 2019
Presented at Armenian Statistics Summer School under Calouste Gulbenkian Travel Grant
Jun 2023
MIT Presidential Fellow
Sep 2019
Elected to Phi Beta Kappa Honors Society
Jun 2019
Research
Covariance alignment: from maximum likelihood estimation to Gromov-Wasserstein
Yanjun Han, Philippe Rigollet, George Stepaniants
arXiv, 2023
Optimal transport for automatic alignment of untargeted metabolomic data
Marie Breeur, George Stepaniants, Pekka Keski-Rahkonen, Philippe Rigollet, Vivian Viallon
eLife, 2024
Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations
George Stepaniants, Alasdair D. Hastewell, Dominic J. Skinner, Jan F. Totz, Jörn Dunkel
PRR, 2024
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces
George Stepaniants
JMLR, 2023
GULP: a prediction-based metric between representations
Enric Boix-Adsera, Hannah Lawrence, George Stepaniants, Philippe Rigollet
NeurIPS, 2022
Fast and smooth interpolation on Wasserstein space
Sinho Chewi, Julien Clancy, Thibaut Le Gouic, Philippe Rigollet, George Stepaniants, Austin Stromme
AISTATS, 2021
Inferring causal networks of dynamical systems through transient dynamics and perturbation
George Stepaniants, Bingni W Brunton, J Nathan Kutz
Physical Review E, 2020
The Lebesgue Integral, Chebyshev's Inequality, and the Weierstrass Approximation Theorem
George Stepaniants
Undergraduate Academic Report, 2017Teaching Philosophy
My goal as an educator is to teach students how to work on the interface of different disciplines and leverage tools from mathematical theory in physics, life sciences, probability theory, and statistics to solve their problems. My teaching philosophy is to train students to
- (1.) Find interesting mathematical ideas or undeveloped theory in esoteric field-specific literature
- (2.) Translate this specialized literature into a well-posed mathematical theory
- (3.) Identify when and how a mathematical theory can be brought to life as a numerical algorithm
I am dedicated to mentoring and student outreach, and am taking important steps in education and research mentorship at Caltech as well as in my cultural Armenian community. I continue to expand my outreach and service in communities that historically have had less access to education in mathematics and science.
Teaching Assistantship
18.032 Differential Equations
18.600 Introduction to Probability
Mentorship and Outreach
California Institute of Technology - Mentorship
Fall 2024
Massachusetts Institute of Technology - Mentorship
Summer 2023 - Fall 2023
Summer 2023
Fall 2021 - Spring 2021
University of Washington - Community Service
2015 - 2019
2015 - 2016
Service and Leadership
2020
2015 - 2019
2015 - 2019
Employment
Sep 2024 - Jun 2027
California Institute of Technology (Posdoctoral Scholar)
NSF Mathematical Sciences Postdoctoral Research Fellow (MSPRF)
Department of Computing and Mathematical Sciences (CMS)Postdoctoral Advisor: Andrew Stuart
Education
Sep 2019 - Jun 2024
Massachusetts Institute of Technology (PhD)
Department of Mathematics and Institute for Data, Systems, and Society (IDSS)PhD Advisors: Philippe Rigollet and Jörn Dunkel
Thesis: Inference from limited observations in statistical, dynamical, and functional problems
GPA: 4.9/5.0
Sep 2015 - Jun 2019
University of Washington, Seattle (BSc)
Department of Mathematics and Department of Computer Science (double major)Undergraduate Research Advisors: Nathan Kutz and Bing Brunton
Research Topic: Inferring causal networks of dynamical systems through transient dynamics and perturbation
GPA: 3.87/4.00
Academic Awards
NSF Mathematical Sciences Postdoctoral Research Fellowship (MSPRF)
Sep 2024 - Jun 2027
IMS Lawrence D. Brown Ph.D. Student Award Recipient
Sep 2024
NSF Graduate Research Fellowship (GRFP)
Sep 2019 - Jun 2024
SIAM Student Travel Award
Dec 2023
Calouste Gulbenkian Foundation Short Term Conference and Travel Grant
Jun 2023
MIT Presidential Fellow
Sep 2019 - Jun 2020
Phi Beta Kappa Honors Society Member
Jun 2019
Mary Gates Research Scholarship (merit-based)
Jun 2019
University of Washington Dean's List
Jun 2016 - Aug 2016
University of Washington Early Acceptance at 16 (UW Academy)
Sep 2015
Publications
Manuscripts in Review
Journal Articles
Conference Proceedings
In Preparation
Talks and Presentations
Organized Symposia
“Minisymposium on Data-Driven Learning of Dynamical Systems from Partial Observations”, SIAM Conference on Mathematics of Data Science, Atlanta, October 2024
Invited Talks
“Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations”, Fourth Symposium on Machine Learning and Dynamical Systems, Fields Institute, July 2024
“Covariance Alignment with Optimal Transport”, Yale Applied Mathematics Seminar, New Haven, April 2024
“Gromov-Wasserstein Theory and Application to Metabolomics”, SIAM Conference on Uncertainty Quantification, Trieste, Italy, February 2024
“Gromov-Wasserstein Theory and Application to Metabolomics”, Statistics and Learning Theory Summer School, Tsaghkadzor, Armenia, July 2023
“Optimal transport for automatic alignment of untargeted metabolomic data”, Harvard Applied Math Graduate Student Seminar, Cambridge, March 2023
“Learning PDEs in a Reproducing Kernel Hilbert Space”, SIAM Conference on Mathematics of Data Science, San Diego, September 2022
“Learning PDEs in a Reproducing Kernel Hilbert Space”, Meeting on Mathematical Statistics, CIRM, Marseille, December 2021
Contributed Talks
“Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations”, Dynamics Days, UC Davis, January 2024
“Learning and predicting complex systems dynamics from single-variable observations”, APS March Meeting, Chicago, March 2022
“Learning PDEs in a Reproducing Kernel Hilbert Space”, LIDS Stats & Tea, MIT, December 2021
“Inferring causal networks of dynamical systems through transient dynamics and perturbation”, Econometrics Lunch, MIT, December 2021
“Fusion of Genetically Incompatible Fungal Cells”, UCLA Computational and Applied Math REU Presentation, IPAM, August 2018
“Quantifying Rupture Risk of Brain Anuerysms”, MATDAT18: NSF Materials and Data Science Hackathon, Alexandria, June 2018
https://matdat18.wordpress.ncsu.edu/files/2018/06/Team12.pdf“Hyperparameter Selection”, AI2 Research Internship Final Presentation, Seattle, August 2017
“Beaker Experimentation Platform”, AI2 Research Internship Midterm Presentation, Seattle, August 2017
“Image Analysis in Parkinson's Research”, Pfizer Research Internship Final Presentation, Cambridge, August 2016
Poster Presentations
“Covariance alignment: from maximum-likelihood estimation to Gromov-Wasserstein”, Cornell ORIE Young Researchers Workshop, Cornell, October 2023
“Inferring causal networks of dynamical systems through transient dynamics and perturbation”, Undergraduate Research Symposium, UW, June 2019
Internship and Research Experience
Jul 2018 - Aug 2018
Computational and Applied Math Research Experience for Undergrads (REU) at UCLA
Undergraduate Researcher in Mycofluidics LabJun 2017 - Sep 2017
Engineering Intern at Allen Institute for Artificial Intelligence (AI2)
Full Stack Development and Data Analysis/VisualizationAug 2016 - Dec 2016
Natural Language Processing Intern at ABBYY
Parser Accuracy ScoringJun 2016 - Aug 2016
Image Analysis Intern at Pfizer
Imaging Algorithms for Automated Brain Slice ImagingProgramming Languages
Python
92%
Matlab
90%
Julia
85%
R
80%
Computational Skills
Image Analysis
AutoDiff (PyTorch)
Cluster Computing
Numerical Analysis
Data Visualization
Adobe Illustrator
Hobbies
- Reading
- History
- Guitar
- Jazz
- Records
- Dancing
- Coffee
Contact
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