Diyora Salimova
ETH Zurich

Address:
Diyora Salimova
Chair for Mathematical Information Science
Department of Information Technology and Electrical Engineering
ETH Zurich
Sternwartstrasse 7
8092 Zürich
Switzerland

Office: Room E 117
Phone: +41 44 632 26 04

E-mail: sdiyora (add "@mins.ee.ethz.ch")

Links: [Profile on ResearchGate] [Profile on GoogleScholar] [Profile on MathSciNet] [Profile on Scopus] [ORCID] [Homepage at ETHZ]

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

  • from 06/2020:          Lecturer at ETH Zurich.
  • from 02/2020:          ETH Foundations of Data Science postdoctoral fellow, ETH Zurich. Mentor: Prof. Dr. Helmut Bölcskei
  • 01/2020:                   Postdoc at ETH Zurich, D-MATH, Seminar for Applied Mathematics

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.
  • 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.
  • Grohs, P., Jentzen, A., and Salimova, D., Deep neural network approximations for Monte Carlo algorithms. [arXiv] (2019), 45 pages. Accepted in Springer Nat. Part. Diff. Equ. Appl.
  • 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)
  • 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