Zobrazeno 1 - 10
of 29
pro vyhledávání: '"von Wurstemberger P"'
This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We provide a d
Externí odkaz:
http://arxiv.org/abs/2412.01371
Autor:
Gonon, Lukas, Jentzen, Arnulf, Kuckuck, Benno, Liang, Siyu, Riekert, Adrian, von Wurstemberger, Philippe
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively studied. One
Externí odkaz:
http://arxiv.org/abs/2408.13222
This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as full
Externí odkaz:
http://arxiv.org/abs/2310.20360
In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN) architectures
Externí odkaz:
http://arxiv.org/abs/2302.03286
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of Monte Carlo (
Externí odkaz:
http://arxiv.org/abs/2202.02717
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we refer to a
Externí odkaz:
http://arxiv.org/abs/2012.04326
Autor:
Becker, Sebastian, Braunwarth, Ramon, Hutzenthaler, Martin, Jentzen, Arnulf, von Wurstemberger, Philippe
Publikováno v:
Commun. Comput. Phys. 28 (2020), no. 5, 2109-2138
One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear partial differential equations (PDEs). In particular, it is very hard to de
Externí odkaz:
http://arxiv.org/abs/2005.10206
Publikováno v:
Electron. J. Probab. 25 (2020), 101
Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial derivatives in
Externí odkaz:
http://arxiv.org/abs/1903.05985
Publikováno v:
Mem. Amer. Math. Soc.284(2023), no.1410, v+93 pp
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and c
Externí odkaz:
http://arxiv.org/abs/1809.02362
Autor:
Hutzenthaler, Martin, Jentzen, Arnulf, Kruse, Thomas, Nguyen, Tuan Anh, von Wurstemberger, Philippe
Publikováno v:
Proceedings of the Royal Society A 476, no. 2244 (2020): 20190630
For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the reciprocal
Externí odkaz:
http://arxiv.org/abs/1807.01212