Diyora Salimova
AlbertLudwigsUniversity of Freiburg
Address:
Junior Prof. Dr. Diyora Salimova
Department for Applied Mathematics
Mathematical Institute
AlbertLudwigsUniversity of Freiburg
HermannHerderStr. 10
79104 Freiburg im Breisgau
Germany
Office: Room 209
Phone: +49 761 2035634
Email: diyora.salimova (add "@mathematik.unifreiburg.de")
Links:
[Profile on ResearchGate]
[Profile on GoogleScholar]
[Profile on MathSciNet]
[Profile on Scopus]
[ORCID]
[Homepage at ETHZ]
[Homepage at the University of Freiburg]
Vacant PhD position
I have an open position for a PhD. Prospective candidates are expected to have a strong mathematical background and be interested in the theory of machine learning. If you are interested, you can approach me via email together with your detailed curriculum vitae and transcripts of grades.
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
 09/201612/2019: Doctor of Sciences of ETH Zurich, Switzerland. PhD supervisor: Prof. Dr. Arnulf Jentzen
 09/201310/2015: Master of Science in Applied Mathematics, ETH Zurich, Switzerland
 09/201106/2013: Bachelor of Science in Mathematics, Jacobs University Bremen, Germany
 09/200906/2011: 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.,
Spacetime deep neural network approximations for highdimensional 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 linearimplicit 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, 11671205.
[arXiv].
 Mazzonetto, S., and Salimova, D.,
Existence, uniqueness, and numerical approximations for stochastic Burgers equations.
Stoch. Anal. Appl. 38 (2020), no. 4, 623646.
[arXiv].
 Jentzen, A., Salimova, D., and Welti, T.,
Strong convergence for explicit spacetime discrete numerical approximation methods for stochastic Burgers equations.
J. Math. Anal. Appl. 469 (2019), no. 2, 661704.
[arXiv].
 Hutzenthaler, M., Jentzen, A., and Salimova, D.,
Strong convergence of fulldiscrete nonlinearitytruncated accelerated exponential Eulertype approximations for stochastic KuramotoSivashinsky equations.
Comm. Math. Sci. 16 (2018), no. 6, 14891529.
[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), 7981.
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
