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A Derivative-Free Method for Solving Elliptic Partial Differential
  Equations with Deep Neural Networks

A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks

Journal of Computational Physics (JCP), 2020
17 January 2020
Jihun Han
Mihai Nica
A. Stinchcombe
ArXiv (abs)PDFHTML

Papers citing "A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks"

15 / 15 papers shown
Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Xinwen Ding
Adam R Stinchcombe
114
0
0
22 Aug 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
324
7
0
07 May 2025
Extremization to Fine Tune Physics Informed Neural Networks for Solving
  Boundary Value Problems
Extremization to Fine Tune Physics Informed Neural Networks for Solving Boundary Value ProblemsCommunications in nonlinear science & numerical simulation (CNSNS), 2024
A. Thiruthummal
Sergiy Shelyag
Eun-Jin Kim
258
5
0
07 Jun 2024
Solving Poisson Equations using Neural Walk-on-Spheres
Solving Poisson Equations using Neural Walk-on-Spheres
Hong Chul Nam
Julius Berner
Anima Anandkumar
285
11
0
05 Jun 2024
Stochastic approach for elliptic problems in perforated domains
Stochastic approach for elliptic problems in perforated domains
Jihun Han
Yoonsang Lee
103
2
0
18 Mar 2024
An analysis of the derivative-free loss method for solving PDEs
An analysis of the derivative-free loss method for solving PDEs
Jihun Han
Yoonsang Lee
186
2
0
28 Sep 2023
Neural Operators for Accelerating Scientific Simulations and Design
Neural Operators for Accelerating Scientific Simulations and DesignNature Reviews Physics (Nat. Rev. Phys.), 2023
Kamyar Azzizadenesheli
Nikola B. Kovachki
Zong-Yi Li
Miguel Liu-Schiaffini
Jean Kossaifi
Anima Anandkumar
AI4CE
825
321
0
27 Sep 2023
An Extreme Learning Machine-Based Method for Computational PDEs in
  Higher Dimensions
An Extreme Learning Machine-Based Method for Computational PDEs in Higher DimensionsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Yiran Wang
Suchuan Dong
383
56
0
13 Sep 2023
A Survey on Solving and Discovering Differential Equations Using Deep
  Neural Networks
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks
Hyeonjung Jung
Jung
Jayant Gupta
B. Jayaprakash
Matthew J. Eagon
Harish Selvam
Carl Molnar
W. Northrop
Shashi Shekhar
AI4CE
334
7
0
26 Apr 2023
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic RepresentationIEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2023
Rui Zhang
Qi Meng
Rongchan Zhu
Yue Wang
Wenlei Shi
Shihua Zhang
Zhi-Ming Ma
Tie-Yan Liu
DiffMAI4CE
951
14
0
10 Feb 2023
A Neural Network Approach for Homogenization of Multiscale Problems
A Neural Network Approach for Homogenization of Multiscale ProblemsMultiscale Modeling & simulation (MMS), 2022
Jihun Han
Yoonsang Lee
243
18
0
04 Jun 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and
  parabolic boundary value problems
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
Nikolas Nusken
Lorenz Richter
PINNDiffM
369
38
0
07 Dec 2021
Hierarchical Learning to Solve Partial Differential Equations Using
  Physics-Informed Neural Networks
Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks
Jihun Han
Yoonsang Lee
AI4CE
303
10
0
02 Dec 2021
An overview on deep learning-based approximation methods for partial
  differential equations
An overview on deep learning-based approximation methods for partial differential equations
C. Beck
Martin Hutzenthaler
Arnulf Jentzen
Benno Kuckuck
693
175
0
22 Dec 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural
  Networks
Numerical Solution of the Parametric Diffusion Equation by Deep Neural NetworksJournal of Scientific Computing (J. Sci. Comput.), 2020
Moritz Geist
P. Petersen
Mones Raslan
R. Schneider
Gitta Kutyniok
255
97
0
25 Apr 2020
1
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