Arnulf Jentzen

115 papers Journal 115

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Physics-informed diffusion models in spectral space. CoRR Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen
2026	J	`jnl`	Uniform a priori bounds and error analysis for the Adam stochastic gradient descent optimization method. CoRR Steffen Dereich, Thang Do, Arnulf Jentzen
2025	J	`jnl`	A brief review of the Deep BSDE method for solving high-dimensional partial differential equations. CoRR Jiequn Han, Arnulf Jentzen, Weinan E
2025	J	`jnl`	Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer. CoRR Steffen Dereich, Thang Do, Arnulf Jentzen, Philippe von Wurstemberger
2025	J	`jnl`	Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality. CoRR Arnulf Jentzen, Konrad Kleinberg, Thomas Kruse
2025	J	`jnl`	Error analysis for the deep Kolmogorov method. CoRR Iulian Cîmpean, Thang Do, Lukas Gonon, Arnulf Jentzen, Ionel Popescu
2025	J	`jnl`	Mathematical analysis of the gradients in deep learning. CoRR Steffen Dereich, Thang Do, Arnulf Jentzen, Frederic Weber
2025	J	`jnl`	Non-convergence to Global Minimizers for Adam and Stochastic Gradient Descent Optimization and Constructions of Local Minimizers in the Training of Artificial Neural Networks. SIAM/ASA J. Uncertain. Quantification Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks. CoRR Thang Do, Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	ODE approximation for the Adam algorithm: General and overparametrized setting. CoRR Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
2025	J	`jnl`	On the logical skills of large language models: evaluations using arbitrarily complex first-order logic problems. CoRR Shokhrukh Ibragimov, Arnulf Jentzen, Benno Kuckuck
2025	J	`jnl`	PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning. CoRR Arnulf Jentzen, Julian Kranz, Adrian Riekert
2025	J	`jnl`	SAD Neural Networks: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures. CoRR Julian Kranz, Davide Gallon, Steffen Dereich, Arnulf Jentzen
2025	J	`jnl`	Sharp higher order convergence rates for the Adam optimizer. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2024	J	`jnl`	An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning. CoRR Lukas Gonon, Arnulf Jentzen, Benno Kuckuck, Siyu Liang, Adrian Riekert, Philippe von Wurstemberger
2024	J	`jnl`	An overview of diffusion models for generative artificial intelligence. CoRR Davide Gallon, Arnulf Jentzen, Philippe von Wurstemberger
2024	J	`jnl`	Convergence rates for the Adam optimizer. CoRR Steffen Dereich, Arnulf Jentzen
2024	J	`jnl`	Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations. CoRR Julia Ackermann, Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett
2024	J	`jnl`	Gradient Descent Provably Escapes Saddle Points in the Training of Shallow ReLU Networks. J. Optim. Theory Appl. Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2024	J	`jnl`	Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2024	J	`jnl`	Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates. CoRR Steffen Dereich, Robin Graeber, Arnulf Jentzen
2024	J	`jnl`	Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks. CoRR Arnulf Jentzen, Adrian Riekert
2024	J	`jnl`	Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation. CoRR Sonja Hannibal, Arnulf Jentzen, Do Minh Thang
2024	J	`jnl`	On the Existence of Minimizers in Shallow Residual ReLU Neural Network Optimization Landscapes. SIAM J. Numer. Anal. Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
2024	J	`jnl`	Weak convergence rates for temporal numerical approximations of the semilinear stochastic wave equation with multiplicative noise. Numerische Mathematik Sonja Cox, Arnulf Jentzen, Felix Lindner
2023	J	`jnl`	Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. CoRR Arnulf Jentzen, Adrian Riekert, Philippe von Wurstemberger
2023	J	`jnl`	An efficient Monte Carlo scheme for Zakai equations. Commun. Nonlinear Sci. Numer. Simul. Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
2023	J	`jnl`	Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the L CoRR Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, Joshua Lee Padgett
2023	J	`jnl`	Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. J. Complex. Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen, Sarah Koppensteiner
2023	J	`jnl`	Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory. CoRR Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
2023	J	`jnl`	On the existence of minimizers in shallow residual ReLU neural network optimization landscapes. CoRR Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
2023	J	`jnl`	Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation. Appl. Math. Comput. Arnulf Jentzen, Timo Welti
2023	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. J. Num. Math. Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen
2023	J	`jnl`	Space-time error estimates for deep neural network approximations for differential equations. Adv. Comput. Math. Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philipp Zimmermann
2023	J	`jnl`	The necessity of depth for artificial neural networks to approximate certain classes of smooth and bounded functions without the curse of dimensionality. CoRR Lukas Gonon, Robin Graeber, Arnulf Jentzen
2022	J	`jnl`	A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. J. Complex. Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek
2022	J	`jnl`	A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions. J. Mach. Learn. Res. Arnulf Jentzen, Adrian Riekert
2022	J	`jnl`	An efficient Monte Carlo scheme for Zakai equations. CoRR Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
2022	J	`jnl`	Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions. CoRR Victor Boussange, Sebastian Becker, Arnulf Jentzen, Benno Kuckuck, Loïc Pellissier
2022	J	`jnl`	Efficient Approximation of High-Dimensional Functions With Neural Networks. IEEE Trans. Neural Networks Learn. Syst. Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2022	J	`jnl`	Gradient descent provably escapes saddle points in the training of shallow ReLU networks. CoRR Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2022	J	`jnl`	Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions. J. Nonlinear Sci. Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2022	J	`jnl`	Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing. CoRR Sebastian Becker, Arnulf Jentzen, Marvin S. Müller, Philippe von Wurstemberger
2022	J	`jnl`	Normalized gradient flow optimization in the training of ReLU artificial neural networks. CoRR Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss
2022	J	`jnl`	On bounds for norms of reparameterized ReLU artificial neural network parameters: sums of fractional powers of the Lipschitz norm control the network parameter vector. CoRR Arnulf Jentzen, Timo Kröger
2022	J	`jnl`	Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities. Found. Comput. Math. Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
2021	J	`jnl`	A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. CoRR Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek
2021	J	`jnl`	A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions. CoRR Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl, Adrian Riekert, Luca Scarpa
2021	J	`jnl`	Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases. CoRR Arnulf Jentzen, Timo Kröger
2021	J	`jnl`	Deep Splitting Method for Parabolic PDEs. SIAM J. Sci. Comput. Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
2021	J	`jnl`	Deep neural network approximation theory for high-dimensional functions. CoRR Pierfrancesco Beneventano, Patrick Cheridito, Robin Graeber, Arnulf Jentzen, Benno Kuckuck
2021	J	`jnl`	Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. CoRR Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss
2021	J	`jnl`	Full history recursive multilevel Picard approximations for ordinary differential equations with expectations. CoRR Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Emilia Magnani
2021	J	`jnl`	Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions. CoRR Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2021	J	`jnl`	Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. CoRR Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen, Sarah Koppensteiner
2021	J	`jnl`	Non-convergence of stochastic gradient descent in the training of deep neural networks. J. Complex. Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2021	J	`jnl`	On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. CoRR Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen
2021	J	`jnl`	Solving the Kolmogorov PDE by Means of Deep Learning. J. Sci. Comput. Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, Arnulf Jentzen
2021	J	`jnl`	Strong L CoRR Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett
2021	J	`jnl`	Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients. Found. Comput. Math. Arnulf Jentzen, Ryan Kurniawan
2020	J	`jnl`	Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning. CoRR Weinan E, Jiequn Han, Arnulf Jentzen
2020	J	`jnl`	An overview on deep learning-based approximation methods for partial differential equations. CoRR Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck
2020	J	`jnl`	Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. SIAM J. Math. Data Sci. Julius Berner, Philipp Grohs, Arnulf Jentzen
2020	J	`jnl`	Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. J. Mach. Learn. Res. Benjamin J. Fehrman, Benjamin Gess, Arnulf Jentzen
2020	J	`jnl`	Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems. CoRR Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
2020	J	`jnl`	Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions. Numer. Algorithms Arnulf Jentzen, Felix Lindner, Primoz Pusnik
2020	J	`jnl`	High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations. CoRR Pierfrancesco Beneventano, Patrick Cheridito, Arnulf Jentzen, Philippe von Wurstemberger
2020	J	`jnl`	Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates. J. Complex. Arnulf Jentzen, Philippe von Wurstemberger
2020	J	`jnl`	Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities. CoRR Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen
2020	J	`jnl`	Non-convergence of stochastic gradient descent in the training of deep neural networks. CoRR Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2020	J	`jnl`	Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations. CoRR Christian Beck, Arnulf Jentzen, Thomas Kruse
2020	J	`jnl`	Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. CoRR Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger
2020	J	`jnl`	Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation. CoRR Arnulf Jentzen, Timo Welti
2020	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. J. Num. Math. Christian Beck, Fabian Hornung, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
2020	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations. CoRR Christian Beck, Lukas Gonon, Arnulf Jentzen
2020	J	`jnl`	Space-time deep neural network approximations for high-dimensional partial differential equations. CoRR Fabian Hornung, Arnulf Jentzen, Diyora Salimova
2020	J	`jnl`	Strong overall error analysis for the training of artificial neural networks via random initializations. CoRR Arnulf Jentzen, Adrian Riekert
2020	J	`jnl`	Weak error analysis for stochastic gradient descent optimization algorithms. CoRR Aritz Bercher, Lukas Gonon, Arnulf Jentzen, Diyora Salimova
2019	J	`jnl`	Convergence rates for the stochastic gradient descent method for non-convex objective functions. CoRR Benjamin J. Fehrman, Benjamin Gess, Arnulf Jentzen
2019	J	`jnl`	Deep Optimal Stopping. J. Mach. Learn. Res. Sebastian Becker, Patrick Cheridito, Arnulf Jentzen
2019	J	`jnl`	Deep neural network approximations for Monte Carlo algorithms. CoRR Philipp Grohs, Arnulf Jentzen, Diyora Salimova
2019	J	`jnl`	Deep splitting method for parabolic PDEs. CoRR Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
2019	J	`jnl`	Efficient approximation of high-dimensional functions with deep neural networks. CoRR Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek
2019	J	`jnl`	Full error analysis for the training of deep neural networks. CoRR Christian Beck, Arnulf Jentzen, Benno Kuckuck
2019	J	`jnl`	Generalised multilevel Picard approximations. CoRR Michael B. Giles, Arnulf Jentzen, Timo Welti
2019	J	`jnl`	Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations. J. Nonlinear Sci. Christian Beck, Weinan E, Arnulf Jentzen
2019	J	`jnl`	On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations. J. Sci. Comput. Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
2019	J	`jnl`	On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. Finance Stochastics Mario Hefter, Arnulf Jentzen
2019	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. CoRR Christian Beck, Fabian Hornung, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
2019	J	`jnl`	Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities. CoRR Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
2019	J	`jnl`	Solving high-dimensional optimal stopping problems using deep learning. CoRR Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Timo Welti
2019	J	`jnl`	Space-time error estimates for deep neural network approximations for differential equations. CoRR Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philipp Zimmermann
2019	J	`jnl`	Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations. CoRR Martin Hutzenthaler, Arnulf Jentzen, Felix Lindner, Primoz Pusnik
2019	J	`jnl`	Towards a regularity theory for ReLU networks - chain rule and global error estimates. CoRR Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen
2019	J	`jnl`	Uniform error estimates for artificial neural network approximations for heat equations. CoRR Lukas Gonon, Philipp Grohs, Arnulf Jentzen, David Kofler, David Siska
2018	J	`jnl`	A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. CoRR Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philippe von Wurstemberger
2018	J	`jnl`	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. CoRR Arnulf Jentzen, Diyora Salimova, Timo Welti
2018	J	`jnl`	Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. CoRR Julius Berner, Philipp Grohs, Arnulf Jentzen
2018	J	`jnl`	Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Math. Comput. Martin Hutzenthaler, Arnulf Jentzen, Xiaojie Wang
2018	J	`jnl`	Solving stochastic differential equations and Kolmogorov equations by means of deep learning. CoRR Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, Arnulf Jentzen
2017	J	`jnl`	Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. CoRR Weinan E, Jiequn Han, Arnulf Jentzen
2017	J	`jnl`	Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. CoRR Christian Beck, Weinan E, Arnulf Jentzen
2017	J	`jnl`	Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning. CoRR Jiequn Han, Arnulf Jentzen, Weinan E
2016	J	`jnl`	An Exponential Wagner-Platen Type Scheme for SPDEs. SIAM J. Numer. Anal. Sebastian Becker, Arnulf Jentzen, Peter E. Kloeden
2015	J	`jnl`	A Milstein Scheme for SPDEs. Found. Comput. Math. Arnulf Jentzen, Michael Röckner
2013	J	`jnl`	Galerkin Approximations for the Stochastic Burgers Equation. SIAM J. Numer. Anal. Dirk Blömker, Arnulf Jentzen
2011	J	`jnl`	Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients. Found. Comput. Math. Martin Hutzenthaler, Arnulf Jentzen
2011	J	`jnl`	Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise. SIAM J. Numer. Anal. Arnulf Jentzen
2010	J	`jnl`	An Improved Maximum Allowable Transfer Interval for L IEEE Trans. Autom. Control. Arnulf Jentzen, Frank Leber, Daniela Schneisgen, Arno Berger, Stefan Siegmund
2009	J	`jnl`	Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients. Numerische Mathematik Arnulf Jentzen, Peter E. Kloeden, Andreas Neuenkirch