48 citations · 151 across the 14 of their papers we have counts for
14 papers
Residual neural networks overcome the curse of dimensionality for semilinear heat equations
Ilkhom Mukhammadiev, Diyora Salimova
Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (P…
Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions
Shokhrukh Ibragimov, Ilkhom Mukhammadiev, Diyora Salimova
In this paper, we study the optimization landscape induced by the true loss for shallow polynomial neural networks (PNNs) with neurons on the hidden l…
Refining Diffusion Models for Motion Synthesis with an Acceleration Loss to Generate Realistic IMU Data
Lars Ole Häusler, Lena Uhlenberg, Göran Köber +2
We propose a text-to-IMU (inertial measurement unit) motion-synthesis framework to obtain realistic IMU data by fine-tuning a pretrained diffusion model with an acceleration-based…
Approximation properties of Residual Neural Networks for Kolmogorov PDEs
Jonas Baggenstos, Diyora Salimova
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 reco…
Weak error analysis for stochastic gradient descent optimization algorithms
Aritz Bercher, Lukas Gonon, Arnulf Jentzen +1
Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization…
Space-time deep neural network approximations for high-dimensional partial differential equations
Fabian Hornung, Arnulf Jentzen, Diyora Salimova
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 approximatio…
Deep neural network approximations for Monte Carlo algorithms
Philipp Grohs, Arnulf Jentzen, Diyora Salimova
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…
Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
Matteo Beccari, Martin Hutzenthaler, Arnulf Jentzen +3
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-dimension…
Existence, uniqueness, and numerical approximations for stochastic Burgers equations
Sara Mazzonetto, Diyora Salimova
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…
Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations
Arnulf Jentzen, Sara Mazzonetto, Diyora Salimova
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 frame…
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
Arnulf Jentzen, Diyora Salimova, Timo Welti
In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, ob…
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
Arnulf Jentzen, Diyora Salimova, Timo Welti
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPD…
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions
Máté Gerencsér, Arnulf Jentzen, Diyora Salimova
In the recent article [Jentzen, A., Müller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow…
Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
Martin Hutzenthaler, Arnulf Jentzen, Diyora Salimova
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white n…