Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts. Broad, wholesome, charitable views of men and things cannot be acquired by vegetating in one little corner of the earth all one's lifetime.
-- Mark Twain


Ilya Timofeyev
Professor
University of Houston
Department of Mathematics
673 Philip G. Hoffman Hall
Houston, TX 77204-3008

Email : ilya at math dot uh dot edu
Office : PGH673

RA positions in data science and stochasic analysis

Presently I have several RA positions in data science and stochastic analysis. The overall question is how to use neural networks/stochastic tools to accelerate numerical simulations of PDEs. The first project is about Generative Neural Networks (GANs) and simulations of PDEs. It is closely related to this paper. The second project is how to use Recurrent Neural Networks (RNNs) to predict solutions of dynamical systems. Here is a preprint on this subject. Finally, I'm also interested in multiscale stochastic analysis and estimating stochastic differential equation from data. Here is a recent paper on this topic.

Please contact me if you're interested in these research topics and I'll be happy to arrange a special topics course.

UH Library,     Academic Calendar.     Data-Enabled Science Seminar

Research Interests

  • applications of machine learning and deep learning for time-series analysis and computational PDEs
  • applied and computational stochastic processes
  • applied mathematics and numerical simulations of partial differential equations
  • stochastic modeling of large scales in fluid dynamics
  • homogenization of partial differential equations - analysis, computations, and data-driven derivation
  • applications of stochastic processes in finance
  • multi-agent spatially extended systems
  • mathematical biology - agent-based modeing, collective behavior of agents, and derivation of coarse-grained systems

    Feel free to contact me if you're interested in one of these researh topics and would like to learn more.

    Research

    A short description of my current research interests can be found here

    Recent Funding

    NSF-NIGMS "Mechanisms of multicellular self-organization in Myxococcus xanthus", 2019-2023, $275,000

    ONR "Sub-grid scale modeling and data-driven model improvement for the shallow-water equations", 2017-2022, $150,000

    Graduate Students and their First Positions

    current - Anton Myshak, Amran Mojamder, Aijaz Nazir, Md Rezwan Bin Mizan (with Prof. M. Olshanskii)
    recent graduates - Shah Alam, Ph.D. (Summer 2024) (co-advised with prof. Ott) Sul Ross State University
    graduated - M. Batista, Ph.D. (Fall 2022) (co-advised with prof. Perepelitsa), CDC,   M. Daneshvar, Ph.D. (Fall 2021),   J. Alcala, Ph.D. (Fall 2021) - Faculty, The University of the Philippines Los Banos,   Xiao Chen, Ph.D. (2021) - Grabel Capital Management,   P. Bedakar, Ph.D. (2020) (co-advisor; advisor: prof. Perepelitsa) - Postdoc, Johns Hopkins U,   Xi Chen, Ph.D. (2020) - Research Associate, Houston Methodist,   D. Saha, Ph.D. (2018) (co-advised with prof R. Azencott) - Data Analyst, GE Energy,   T. Weber, PhD. (2016) (co-advised with prof. Ott) - Instructor, UH,   P. Ren, Ph.D. (2014) (co-advised with prof. R. Azencott) - Zion Bank, Salt-Lake City, UT,   A. Jain, Ph.D. (2012) - Data Analyst, Accolade,   A. Beri, Ph.D. (2010) (co-advised with prof. R. Azencott) - Senior Quantitative Analyst, CRISIL,   N. Barlas, Ph.D. (2009) - Analyst, USAA,   K. Nimsaila, Ph.D. (2009) - Analyst, CGGVeritas