Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems
Fuente:
arXiv
Saved in:
| Main Authors: | Dereich, Steffen, Jentzen, Arnulf, Riekert, Adrian |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses
by: Dereich, Steffen, et al.
Published: (2024)
by: Dereich, Steffen, et al.
Published: (2024)
PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning
by: Jentzen, Arnulf, et al.
Published: (2025)
by: Jentzen, Arnulf, et al.
Published: (2025)
Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks
by: Jentzen, Arnulf, et al.
Published: (2024)
by: Jentzen, Arnulf, et al.
Published: (2024)
On the existence of minimizers in shallow residual ReLU neural network optimization landscapes
by: Dereich, Steffen, et al.
Published: (2023)
by: Dereich, Steffen, et al.
Published: (2023)
Sharp higher order convergence rates for the Adam optimizer
by: Dereich, Steffen, et al.
Published: (2025)
by: Dereich, Steffen, et al.
Published: (2025)
Convergence rates for the Adam optimizer
by: Dereich, Steffen, et al.
Published: (2024)
by: Dereich, Steffen, et al.
Published: (2024)
Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks
by: Do, Thang, et al.
Published: (2025)
by: Do, Thang, et al.
Published: (2025)
Asymptotic stability properties and a priori bounds for Adam and other gradient descent optimization methods
by: Dereich, Steffen, et al.
Published: (2025)
by: Dereich, Steffen, et al.
Published: (2025)
ODE approximation for the Adam algorithm: General and overparametrized setting
by: Dereich, Steffen, et al.
Published: (2025)
by: Dereich, Steffen, et al.
Published: (2025)
Martingale deep learning for very high dimensional quasi-linear partial differential equations and stochastic optimal controls
by: Cai, Wei, et al.
Published: (2024)
by: Cai, Wei, et al.
Published: (2024)
Space-time deep neural network approximations for high-dimensional partial differential equations
by: Hornung, Fabian, et al.
Published: (2020)
by: Hornung, Fabian, et al.
Published: (2020)
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
by: Jentzen, Arnulf, et al.
Published: (2023)
by: Jentzen, Arnulf, et al.
Published: (2023)
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
by: Do, Thang, et al.
Published: (2024)
by: Do, Thang, et al.
Published: (2024)
Uniform a priori bounds and error analysis for the Adam stochastic gradient descent optimization method
by: Dereich, Steffen, et al.
Published: (2026)
by: Dereich, Steffen, et al.
Published: (2026)
Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates
by: Dereich, Steffen, et al.
Published: (2024)
by: Dereich, Steffen, et al.
Published: (2024)
Iterative solvers for partial differential equations with dissipative structure: Operator preconditioning and optimal control
by: Mehrmann, Volker, et al.
Published: (2025)
by: Mehrmann, Volker, et al.
Published: (2025)
Two-scale neural networks for optimal control of linear convection-dominated equations
by: Liu, Sijing, et al.
Published: (2026)
by: Liu, Sijing, et al.
Published: (2026)
Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer
by: Dereich, Steffen, et al.
Published: (2025)
by: Dereich, Steffen, et al.
Published: (2025)
Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability
by: Ibragimov, Shokhrukh, et al.
Published: (2022)
by: Ibragimov, Shokhrukh, et al.
Published: (2022)
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
by: Beneventano, Pierfrancesco, et al.
Published: (2020)
by: Beneventano, Pierfrancesco, et al.
Published: (2020)
On the existence of optimal shallow feedforward networks with ReLU activation
by: Dereich, Steffen, et al.
Published: (2023)
by: Dereich, Steffen, et al.
Published: (2023)
Contractivity of neural ODEs: an eigenvalue optimization problem
by: Guglielmi, Nicola, et al.
Published: (2024)
by: Guglielmi, Nicola, et al.
Published: (2024)
Ordinary differential equations for regularized variational problems involving semi-discrete optimal transport
by: Cances, Adrien, et al.
Published: (2026)
by: Cances, Adrien, et al.
Published: (2026)
Convergence analysis for an implementable scheme to solve the linear-quadratic stochastic optimal control problem with stochastic wave equation
by: Chaudhary, Abhishek
Published: (2025)
by: Chaudhary, Abhishek
Published: (2025)
An accelerated gradient method with adaptive restart for convex multiobjective optimization problems
by: Luo, Hao, et al.
Published: (2025)
by: Luo, Hao, et al.
Published: (2025)
Numerical approximations for partially observed optimal control of stochastic partial differential equations
by: Bao, Feng, et al.
Published: (2025)
by: Bao, Feng, et al.
Published: (2025)
A finite element scheme for an optimal control problem on steady Navier-Stokes-Brinkman equations
by: Araneda, Jorge Aguayo, et al.
Published: (2025)
by: Araneda, Jorge Aguayo, et al.
Published: (2025)
An approximate Itô-SDE based simulated annealing algorithm for multivariate design optimization problems
by: Batou, A.
Published: (2019)
by: Batou, A.
Published: (2019)
Unidimensional semi-discrete partial optimal transport
by: Cances, Adrien, et al.
Published: (2025)
by: Cances, Adrien, et al.
Published: (2025)
Modelling sand ripples in mine countermeasure simulations by means of stochastic optimal control
by: Blondeel, Philippe, et al.
Published: (2024)
by: Blondeel, Philippe, et al.
Published: (2024)
Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks
by: Bélières--Frendo, Amaury, et al.
Published: (2024)
by: Bélières--Frendo, Amaury, et al.
Published: (2024)
Error analysis for stochastic gradient optimization schemes using modified equations
by: Bréhier, Charles-Edouard, et al.
Published: (2024)
by: Bréhier, Charles-Edouard, et al.
Published: (2024)
Non-overlapping Schwarz methods in time for parabolic optimal control problems
by: Gander, Martin Jakob, et al.
Published: (2024)
by: Gander, Martin Jakob, et al.
Published: (2024)
Characterizing and computing solutions to regularized semi-discrete optimal transport via an ordinary differential equation
by: Nenna, Luca, et al.
Published: (2025)
by: Nenna, Luca, et al.
Published: (2025)
Anderson-type acceleration method for Deep Neural Network optimization
by: Ito, Kazufumi, et al.
Published: (2025)
by: Ito, Kazufumi, et al.
Published: (2025)
Deep learning based numerical approximation algorithms for stochastic partial differential equations
by: Beck, Christian, et al.
Published: (2020)
by: Beck, Christian, et al.
Published: (2020)
H2 optimal rational approximation on general domains
by: Borghi, Alessandro, et al.
Published: (2023)
by: Borghi, Alessandro, et al.
Published: (2023)
An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction
by: Wen, Tianshu, et al.
Published: (2024)
by: Wen, Tianshu, et al.
Published: (2024)
Numerical solution of elliptic distributed optimal control problems with boundary value tracking
by: Langer, Ulrich, et al.
Published: (2025)
by: Langer, Ulrich, et al.
Published: (2025)
From PDEs constrained optimization to controllability problems via time domain decomposition
by: Cocquet, Pierre-Henri, et al.
Published: (2026)
by: Cocquet, Pierre-Henri, et al.
Published: (2026)
Similar Items
-
Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses
by: Dereich, Steffen, et al.
Published: (2024) -
PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning
by: Jentzen, Arnulf, et al.
Published: (2025) -
Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks
by: Jentzen, Arnulf, et al.
Published: (2024) -
On the existence of minimizers in shallow residual ReLU neural network optimization landscapes
by: Dereich, Steffen, et al.
Published: (2023) -
Sharp higher order convergence rates for the Adam optimizer
by: Dereich, Steffen, et al.
Published: (2025)