Diyora Salimova
University of Freiburg
Address:
Junior Prof. Dr. Diyora Salimova
Department for Applied Mathematics
Mathematical Institute
University of Freiburg
HermannHerderStr. 10, Room 208
79104 Freiburg im Breisgau
Germany
Phone: +49 761 2035634
Office hours: by appointment
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]
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. Accepted in 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.
 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)
 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, 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:
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
 Winter semester 2022/2023: Numerik I 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 EichstättIngolstadt
 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 nonstandard assumptions"
at the
13th International Conference in Monte Carlo & QuasiMonte 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
