Diyora Salimova

Diyora Salimova
University of Freiburg | Albert-Ludwigs-Universität Freiburg · Faculty of Mathematics and Physics

Doctor of Sciences (Dr. sc.)

About

16
Publications
2,661
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175
Citations
Additional affiliations
January 2020 - present
ETH Zurich
Position
  • PostDoc Position
December 2015 - January 2020
ETH Zurich
Position
  • Research Assistant
Education
September 2016 - November 2019
ETH Zurich
Field of study
  • Applied Mathematics
September 2013 - October 2015
ETH Zurich
Field of study
  • Applied Mathematics
September 2011 - June 2013
Jacobs University
Field of study
  • Mathematics

Publications

Publications (16)
Article
Full-text available
In the past few years deep artificial neural networks (DNNs) have been successfully employed in a large number of computational problems including, e.g., language processing, image recognition, fraud detection, and computational advertisement. Recently, it has also been proposed in the scientific literature to reformulate high-dimensional partial d...
Preprint
Full-text available
In recent years residual neural networks (ResNets) as introduced by [He, K., Zhang, X., Ren, S., and Sun, J., Proceedings of the IEEE conference on computer vision and pattern recognition (2016), 770-778] have become very popular in a large number of applications, including in image classification and segmentation. They provide a new perspective in...
Preprint
Full-text available
Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving natural language processing, object and face recognition, fraud detection, computational advertisement, and num...
Preprint
Full-text available
It is one of the most challenging issues in applied mathematics to approximately solve high-dimensional partial differential equations (PDEs) and most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality in the sense that the number of computational operations employed in the...
Article
Full-text available
In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time dis...
Thesis
Full-text available
The main topic of this thesis is to prove approximation results for PDEs. More specifically, in this PhD thesis and in the research articles which are incorporated in this PhD thesis, respectively, we introduce an explicit space-time discrete nume- rical approximation scheme for semilinear stochastic PDEs (SPDEs) and establish its strong convergenc...
Preprint
Full-text available
Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are also a few results in the literature which prove that DNNs can approximate solutions of certain PDEs without the curse of dimensionality in the sense that the number of...
Preprint
Full-text available
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing nonlinearities. It remained an open question whether such a divergence phenomenon also holds in t...
Preprint
Full-text available
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existent fully explicit space-time discre...
Preprint
Full-text available
In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite dimensional ordinary differential equations (ODEs), semilinear deterministic partial differential equations (PDE...
Preprint
Full-text available
In recent years deep artificial neural networks (DNNs) have very successfully been employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of partial differential equations...
Article
Full-text available
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic Burgers equation with space-time white noise. The main result of this paper proves that the proposed...
Article
Full-text available
In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) with infinitely often differenti...
Article
Full-text available
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly non-globally monotone nonlinearities such as stochastic Kuramoto-Sivashinsky equations. The ma...