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An overview on deep learning-based approximation methods for partial
  differential equations
v1v2v3 (latest)

An overview on deep learning-based approximation methods for partial differential equations

22 December 2020
C. Beck
Martin Hutzenthaler
Arnulf Jentzen
Benno Kuckuck
ArXiv (abs)PDFHTML

Papers citing "An overview on deep learning-based approximation methods for partial differential equations"

50 / 62 papers shown
Convomem Benchmark: Why Your First 150 Conversations Don't Need RAG
Convomem Benchmark: Why Your First 150 Conversations Don't Need RAGJournal of the mechanics and physics of solids (JMPS), 2025
Egor Pakhomov
Erik Nijkamp
Caiming Xiong
387
3
0
13 Nov 2025
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Bangti Jin
Longjun Wu
183
1
0
29 Aug 2025
Error analysis for the deep Kolmogorov method
Error analysis for the deep Kolmogorov method
Iulian Cîmpean
Thang Do
Lukas Gonon
Arnulf Jentzen
Ionel Popescu
224
0
0
23 Aug 2025
Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity
Universal Fourier Neural Operators for periodic homogenization problems in linear elasticityJournal of the mechanics and physics of solids (JMPS), 2025
Binh Huy Nguyen
Matti Schneider
AI4CE
314
0
0
16 Jul 2025
PCG-Informed Neural Solvers for High-Resolution Homogenization of Periodic Microstructures
PCG-Informed Neural Solvers for High-Resolution Homogenization of Periodic Microstructures
Yu Xing
Yang Liu
L. Chen
Huiping Tang
Lin Lu
AI4CE
215
1
0
20 Jun 2025
PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning
PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning
Arnulf Jentzen
Julian Kranz
Adrian Riekert
ODL
353
0
0
28 May 2025
A deep solver for backward stochastic Volterra integral equations
A deep solver for backward stochastic Volterra integral equations
Kristoffer Andersson
Alessandro Gnoatto
Camilo Andrés García Trillos
315
3
0
23 May 2025
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han
Arnulf Jentzen
Weinan E
AI4CE
319
6
0
07 May 2025
FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing Flows and the Feynman-Kac Formula
FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing Flows and the Feynman-Kac Formula
Naoufal El Bekri
Lucas Drumetz
Franck Vermet
302
1
0
14 Mar 2025
Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks
Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks
Thang Do
Arnulf Jentzen
Adrian Riekert
322
4
0
03 Mar 2025
An Iterative Deep Ritz Method for Monotone Elliptic Problems
An Iterative Deep Ritz Method for Monotone Elliptic ProblemsJournal of Computational Physics (JCP), 2025
Tianhao Hu
Bangti Jin
Fengru Wang
233
1
0
28 Jan 2025
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$-sense
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in LpL^pLp-sense
Ariel Neufeld
Tuan Anh Nguyen
381
1
0
30 Sep 2024
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer
Georgios Is. Detorakis
526
0
0
21 Aug 2024
DeepNetBeam: A Framework for the Analysis of Functionally Graded Porous
  Beams
DeepNetBeam: A Framework for the Analysis of Functionally Graded Porous Beams
M. Eshaghi
M. Bamdad
C. Anitescu
Yizheng Wang
X. Zhuang
Timon Rabczuk
AI4CE
285
25
0
04 Aug 2024
META-ANOVA: Screening interactions for interpretable machine learning
META-ANOVA: Screening interactions for interpretable machine learningJournal of the Korean Statistical Society (JKSS), 2024
Daniel A. Serino
Marc L. Klasky
Chanmoo Park
Dongha Kim
Yongdai Kim
301
5
0
02 Aug 2024
Neural networks in non-metric spaces
Neural networks in non-metric spaces
Luca Galimberti
327
2
0
13 Jun 2024
Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks
Gradient Flow Based Phase-Field Modeling Using Separable Neural NetworksComputer Methods in Applied Mechanics and Engineering (CMAME), 2024
R. Mattey
Susanta Ghosh
AI4CE
264
3
0
09 May 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEsCommunications in nonlinear science & numerical simulation (CNSNS), 2024
Ariel Neufeld
Philipp Schmocker
Sizhou Wu
638
13
0
08 May 2024
Derivative-based regularization for regression
Derivative-based regularization for regression
Enrico Lopedoto
Maksim Shekhunov
Vitaly Aksenov
K. Salako
Tillman Weyde
282
0
0
01 May 2024
Macroscopic auxiliary asymptotic preserving neural networks for the
  linear radiative transfer equations
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations
Hongyan Li
Song Jiang
Wenjun Sun
Liwei Xu
Guanyu Zhou
237
6
0
04 Mar 2024
Bayesian Differentiable Physics for Cloth Digitalization
Bayesian Differentiable Physics for Cloth Digitalization
Deshan Gong
Ningtao Mao
He Wang
AI4CE
483
4
0
27 Feb 2024
OmniArch: Building Foundation Model For Scientific Computing
OmniArch: Building Foundation Model For Scientific Computing
Tianyu Chen
Haoyi Zhou
Ying Li
Hao Wang
Chonghan Gao
Rongye Shi
Shanghang Zhang
Jianxin Li
AI4CE
397
0
0
25 Feb 2024
A PNP ion channel deep learning solver with local neural network and
  finite element input data
A PNP ion channel deep learning solver with local neural network and finite element input data
Hwi Lee
Zhen Chao
Harris Cobb
Yingjie Liu
Dexuan Xie
170
0
0
31 Jan 2024
Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study
Error Analysis of Option Pricing via Deep PDE Solvers: Empirical StudyIIAI International Conference on Advanced Applied Informatics (IIAI-AAI), 2023
Rawin Assabumrungrat
Kentaro Minami
Masanori Hirano
172
2
0
13 Nov 2023
Drift Control of High-Dimensional RBM: A Computational Method Based on
  Neural Networks
Drift Control of High-Dimensional RBM: A Computational Method Based on Neural Networks
B. Ata
J. M. Harrison
Nian Si
189
4
0
20 Sep 2023
Advances in machine-learning-based sampling motivated by lattice quantum
  chromodynamics
Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicsNature Reviews Physics (Nat. Rev. Phys.), 2023
Kyle Cranmer
G. Kanwar
S. Racanière
Danilo Jimenez Rezende
P. Shanahan
AI4CE
302
37
0
03 Sep 2023
Solving Elliptic Optimal Control Problems via Neural Networks and
  Optimality System
Solving Elliptic Optimal Control Problems via Neural Networks and Optimality SystemAdvances in Computational Mathematics (Adv. Comput. Math.), 2023
Yongcheng Dai
Bangti Jin
R. Sau
Zhi Zhou
304
9
0
23 Aug 2023
From continuous-time formulations to discretization schemes: tensor
  trains and robust regression for BSDEs and parabolic PDEs
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEsJournal of machine learning research (JMLR), 2023
Lorenz Richter
Leon Sallandt
Nikolas Nusken
290
8
0
28 Jul 2023
On Physical Origins of Learning
On Physical Origins of Learning
Alex Ushveridze
AI4CE
200
0
0
27 Jul 2023
Capturing the Diffusive Behavior of the Multiscale Linear Transport
  Equations by Asymptotic-Preserving Convolutional DeepONets
Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONetsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Keke Wu
Xiongbin Yan
Shi Jin
Zheng Ma
414
11
0
28 Jun 2023
Global Convergence of Deep Galerkin and PINNs Methods for Solving
  Partial Differential Equations
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations
Deqing Jiang
Justin A. Sirignano
Samuel N. Cohen
235
10
0
10 May 2023
Physics-informed radial basis network (PIRBN): A local approximating
  neural network for solving nonlinear PDEs
Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs
Jinshuai Bai
Guirong Liu
Ashish Gupta
Laith Alzubaidi
Xinzhu Feng
Yuantong T. Gu
PINN
277
1
0
13 Apr 2023
Multilevel CNNs for Parametric PDEs
Multilevel CNNs for Parametric PDEsJournal of machine learning research (JMLR), 2023
Cosmas Heiß
Ingo Gühring
Martin Eigel
AI4CE
475
12
0
01 Apr 2023
Efficient Sampling of Stochastic Differential Equations with Positive
  Semi-Definite Models
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite ModelsNeural Information Processing Systems (NeurIPS), 2023
Anant Raj
Umut Simsekli
Alessandro Rudi
DiffM
464
3
0
30 Mar 2023
Probing optimisation in physics-informed neural networks
Probing optimisation in physics-informed neural networks
Nayara Fonseca
V. Guidetti
Will Trojak
188
1
0
27 Mar 2023
Quantile and moment neural networks for learning functionals of
  distributions
Quantile and moment neural networks for learning functionals of distributions
X. Warin
156
2
0
20 Mar 2023
Achieving High Accuracy with PINNs via Energy Natural Gradients
Achieving High Accuracy with PINNs via Energy Natural GradientsInternational Conference on Machine Learning (ICML), 2023
Johannes Müller
Marius Zeinhofer
381
12
0
25 Feb 2023
Simultaneous upper and lower bounds of American option prices with
  hedging via neural networks
Simultaneous upper and lower bounds of American option prices with hedging via neural networksSocial Science Research Network (SSRN), 2023
Ivan Guo
Nicolas Langrené
Jiahao Wu
319
4
0
24 Feb 2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher
  order deep operator learning for parametric partial differential equations
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
Arnulf Jentzen
Adrian Riekert
Philippe von Wurstemberger
436
1
0
07 Feb 2023
On Existence Theorems for Conditional Inferential Models
On Existence Theorems for Conditional Inferential Models
Rongrong Zhang
M. Zhu
Chuan-cai Liu
248
0
0
12 Jan 2023
Mean-field neural networks-based algorithms for McKean-Vlasov control
  problems *
Mean-field neural networks-based algorithms for McKean-Vlasov control problems *
Huyen Pham
X. Warin
304
16
0
22 Dec 2022
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator
  Splitting
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator SplittingJournal of Computational Physics (JCP), 2022
Yuan Lan
Zerui Li
Jie Sun
Yang Xiang
210
13
0
11 Dec 2022
Physics-Informed Machine Learning: A Survey on Problems, Methods and
  Applications
Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications
Zhongkai Hao
Songming Liu
Yichi Zhang
Chengyang Ying
Yao Feng
Hang Su
Jun Zhu
PINNAI4CE
453
164
0
15 Nov 2022
Mean-field neural networks: learning mappings on Wasserstein space
Mean-field neural networks: learning mappings on Wasserstein spaceNeural Networks (NN), 2022
H. Pham
X. Warin
351
20
0
27 Oct 2022
$r-$Adaptive Deep Learning Method for Solving Partial Differential
  Equations
r−r-r−Adaptive Deep Learning Method for Solving Partial Differential Equations
Ángel J. Omella
David Pardo
AI4CE
285
4
0
19 Oct 2022
Deep neural network expressivity for optimal stopping problems
Deep neural network expressivity for optimal stopping problemsFinance and Stochastics (Fin. Stoch.), 2022
Lukas Gonon
314
13
0
19 Oct 2022
Jensen-Shannon Divergence Based Novel Loss Functions for Bayesian Neural
  Networks
Jensen-Shannon Divergence Based Novel Loss Functions for Bayesian Neural NetworksNeurocomputing (Neurocomputing), 2022
Ponkrshnan Thiagarajan
Susanta Ghosh
BDL
300
23
0
23 Sep 2022
Deep learning approximations for non-local nonlinear PDEs with Neumann
  boundary conditions
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
V. Boussange
S. Becker
Arnulf Jentzen
Benno Kuckuck
Loïc Pellissier
236
20
0
07 May 2022
Pricing options on flow forwards by neural networks in Hilbert space
Pricing options on flow forwards by neural networks in Hilbert spaceSocial Science Research Network (SSRN), 2022
F. Benth
Nils Detering
Luca Galimberti
278
11
0
17 Feb 2022
Temporal Difference Learning with Continuous Time and State in the
  Stochastic Setting
Temporal Difference Learning with Continuous Time and State in the Stochastic Setting
Ziad Kobeissi
Francis R. Bach
OffRL
304
4
0
16 Feb 2022
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