photo Diyora Salimova
University of Freiburg

Address:
Junior Prof. Dr. Diyora Salimova
Department for Applied Mathematics
Mathematical Institute
University of Freiburg
Hermann-Herder-Str. 10, Room 208
79104 Freiburg im Breisgau
Germany

Phone: +49 761 203-5634

E-mail: diyora.salimova (add "@mathematik.uni-freiburg.de")

Links: [Profile on ResearchGate] [Profile on GoogleScholar] [Profile on MathSciNet] [Profile on Scopus] [ORCID] [Homepage at ETHZ] [Homepage at the University of Freiburg]

Research interests

  • approximation properties of deep neural networks, mathematics for deep learning, machine learning, stochastic gradient descent methods, computational stochastics/stochastic numerics, stochastic differential equations, stochastic analysis, numerical analysis, learning dynamical systems

Positions

Education

  • 09/2016-12/2019:     Doctor of Sciences of ETH Zurich, Switzerland. PhD supervisor: Prof. Dr. Arnulf Jentzen
  • 09/2013-10/2015:     Master of Science in Applied Mathematics, ETH Zurich, Switzerland
  • 09/2011-06/2013:     Bachelor of Science in Mathematics, Jacobs University Bremen, Germany
  • 09/2009-06/2011:     Completed two years of study in undergraduate Mathematics, Samarkand State University, Uzbekistan

Preprints

(authors listed in alphabetical order)
  • Baggenstos, J., and Salimova, D., Approximation properties of Residual Neural Networks for Kolmogorov PDEs. [arXiv] (2021), 24 pages. Revision requested from Discrete Contin. Dyn. Syst. Ser. B.
  • Bercher, A., Gonon, L., Jentzen, A., and Salimova, D., Weak error analysis for stochastic gradient descent optimization algorithms. [arXiv] (2020), 123 pages. Revision requested from Springer Lect. Notes Math.
  • Hornung, F., Jentzen, A., and Salimova, D., Space-time deep neural network approximations for high-dimensional partial differential equations. [arXiv] (2020), 52 pages.
  • Beccari, M., Hutzenthaler, M., Jentzen, A., Kurniawan, R., Lindner, F., and Salimova, D., Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities. [arXiv] (2019), 65 pages.
  • Jentzen, A., Mazzonetto, S., and Salimova, D., Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations. [arXiv] (2018), 28 pages.

Published papers

(authors listed in alphabetical order)
  • Grohs, P., Jentzen, A., and Salimova, D., Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. Partial Differ. Equ. Appl. 3 (2022), no. 4, Paper No. 45. [arXiv]
  • Jentzen, A., Salimova, D., and Welti, T., A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. Comm. Math. Sci. 19 (2021), no. 5, 1167-1205. [arXiv].
  • Mazzonetto, S., and Salimova, D., Existence, uniqueness, and numerical approximations for stochastic Burgers equations. Stoch. Anal. Appl. 38 (2020), no. 4, 623-646. [arXiv].
  • Jentzen, A., Salimova, D., and Welti, T., Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. J. Math. Anal. Appl. 469 (2019), no. 2, 661-704. [arXiv].
  • Hutzenthaler, M., Jentzen, A., and Salimova, D., Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. Comm. Math. Sci. 16 (2018), no. 6, 1489-1529. [arXiv].
  • Gerencsér, M., Jentzen, A., and Salimova, D., On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. Proc. Roy. Soc. London A 473 (2017). [arXiv].
  • Ibragimov, Z. and Salimova, D., On an inequality in l_p(C) involving Basel problem. Elem. Math. 70 (2015), 79-81.

Teaching

  • Fall 2020: Lecturer and course administrator for Numerical Analysis of Stochastic Ordinary Differential Equations at ETH Zurich (alternative course title: “Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods”)
  • Summer semester 2022: Seminar "Approximation Properties of Neural Networks" at University of Freiburg

Invited Research Talks

  • 08/2022:     2022 Workshops on Theory of Machine Learning, Chalmers University, Gothenburg, Sweden
  • 07/2022:     Continuous Time Methods for Machine Learning workshop, ICML 2022, Baltimore, Maryland USA
  • 02/2022:     Oberseminar Angewandte Mathematik, University of Freiburg
  • 09/2021:     Section ''Stochastics and Financial Mathematics" at the German Mathematical Society and the Austrian Mathematical Society (DMV ÖMG) Annual Conference 2021
  • 08/2021:     Special session ''Stochastic Computation and Complexity" at the 13th International Conference on Monte Carlo Methods and Applications (MCM)
  • 02/2021:     Applied Mathematics Seminar, KU Eichstätt-Ingolstadt
  • 11/2020:     Oxford Stochastic Analysis and Mathematical Finance Seminar
  • 04/2019:     Numerical Analysis Seminar, University of Geneva, Switzerland
  • 03/2019:     Research Seminar in Mathematics for Economics and Business, WU Vienna, Austria
  • 03/2019:     Seminar Talk, EPFL Lausanne, Switzerland
  • 09/2018:     Austrian Stochastics Days 2018, Vienna, Austria
  • 07/2018:     Special session ''Numerical approximation of SDEs under non-standard assumptions" at the 13th International Conference in Monte Carlo & Quasi-Monte Carlo in Scientific Computing (MCQMC), Rennes, France
  • 07/2017:     Special session Stochastic Computation workshop at the Foundation of Computational Mathematics (FoCM) conference 2017, Barcelona, Spain