Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Arnulf Jentzen"'
Publikováno v:
Electronic Research Archive, Vol 31, Iss 5, Pp 2519-2554 (2023)
The training of artificial neural networks (ANNs) with rectified linear unit (ReLU) activation via gradient descent (GD) type optimization schemes is nowadays a common industrially relevant procedure. GD type optimization schemes can be regarded as t
Externí odkaz:
https://doaj.org/article/1bb24b33ff194f1ca852c722b785ee8d
Publikováno v:
IEEE Transactions on Neural Networks and Learning Systems, 33 (7)
In this article, we develop a framework for showing that neural networks can overcome the curse of dimensionality in different high-dimensional approximation problems. Our approach is based on the notion of a catalog network, which is a generalizatio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4df6fc7f7d70bb76c8d410df6a500658
https://doi.org/10.1109/tnnls.2021.3049719
https://doi.org/10.1109/tnnls.2021.3049719
Publikováno v:
Advances in Computational Mathematics, 49 (1), Art.-Nr.: 4
Advances in Computational Mathematics, 49 (1)
Advances in Computational Mathematics, 49 (1)
Over the last few years deep artificial neural networks (ANNs) have very successfully been used in numerical simulations for a wide variety of computational problems including computer vision, image classification, speech recognition, natural languag
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56eaa1580b1d4f623e45e0a9f9de4ce5
https://publikationen.bibliothek.kit.edu/1000155432/150164689
https://publikationen.bibliothek.kit.edu/1000155432/150164689
Publikováno v:
Nonlinearity. 35:278-310
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01ca780fa6765a76986169feec76c244
https://doi.org/10.1088/1361-6544/ac337f
https://doi.org/10.1088/1361-6544/ac337f
Publikováno v:
Foundations of Computational Mathematics, 2 (4)
Partial differential equations (PDEs) are a fundamental tool in the modeling of many real-world phenomena. In a number of such real-world phenomena the PDEs under consideration contain gradient-dependent nonlinearities and are high-dimensional. Such
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a47036d02e72ca4b0a06464c031b0b8
https://doi.org/10.1007/s10208-021-09514-y
https://doi.org/10.1007/s10208-021-09514-y
Autor:
Arnulf Jentzen, Timo Welti
Publikováno v:
Applied Mathematics and Computation, 455
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce useful result
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::103175e1e90ae6a47e08ba0a3bb8af25
https://doi.org/10.1016/j.amc.2023.127907
https://doi.org/10.1016/j.amc.2023.127907
Publikováno v:
Communications in Mathematical Sciences. 19:1167-1205
In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detectio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e2250fa531ee39f39af1c462b5ba2629
https://doi.org/10.4310/cms.2021.v19.n5.a1
https://doi.org/10.4310/cms.2021.v19.n5.a1
Publikováno v:
Partial Differential Equations and Applications, 3 (4)
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. Recent
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::936c16cab2f75690252e8e59117cda69
https://doi.org/10.1007/s42985-021-00100-z
https://doi.org/10.1007/s42985-021-00100-z
Publikováno v:
Numerical Algorithms. 85:1447-1473
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical approximat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::edcdfb318b7597f67066ad5a383aeb72
https://doi.org/10.1007/s11075-019-00871-y
https://doi.org/10.1007/s11075-019-00871-y
Publikováno v:
IMA Journal of Numerical Analysis, 41 (1)
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove for every
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a18dea3fbfac8c66288a60714ff4538d
https://doi.org/10.1093/imanum/drz055
https://doi.org/10.1093/imanum/drz055