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Solving high-dimensional eigenvalue problems using deep neural networks:
  A diffusion Monte Carlo like approach
v1v2 (latest)

Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach

Journal of Computational Physics (JCP), 2020
7 February 2020
Jiequn Han
Jianfeng Lu
Mo Zhou
    DiffM
ArXiv (abs)PDFHTML

Papers citing "Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach"

35 / 35 papers shown
Learning Eigenstructures of Unstructured Data Manifolds
Learning Eigenstructures of Unstructured Data Manifolds
Roy Velich
Arkadi Piven
David Bensaid
Daniel Cremers
Thomas Dagès
Ron Kimmel
110
0
0
30 Nov 2025
NeuMatC: A General Neural Framework for Fast Parametric Matrix Operation
NeuMatC: A General Neural Framework for Fast Parametric Matrix Operation
Chuan Wang
Xi-le Zhao
Zhilong Han
Liang Li
Deyu Meng
Michael K. Ng
116
0
0
28 Nov 2025
STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem
STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem
Hong Wang
Jiang Yixuan
Jie Wang
Xinyi Li
Jian Luo
Huanshuo Dong
166
1
0
28 Oct 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
184
1
0
29 Aug 2025
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
Haoxuan Chen
Yinuo Ren
Martin Renqiang Min
Lexing Ying
Zachary Izzo
DiffMMedIm
548
15
0
04 Jun 2025
Rethinking Neural-based Matrix Inversion: Why can't, and Where can
Rethinking Neural-based Matrix Inversion: Why can't, and Where canInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2025
Yuliang Ji
Jian Wu
Yuanzhe Xi
132
1
0
31 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
324
7
0
07 May 2025
From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs
From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs
Rohan Bhatnagar
Ling Liang
Krish Patel
Haizhao Yang
338
3
0
13 Mar 2025
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression MethodJournal of Computational Physics (JCP), 2024
Gareth Hardwick
Senwei Liang
Haizhao Yang
378
3
0
01 Oct 2024
Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems
Score-based Neural Ordinary Differential Equations for Computing Mean Field Control ProblemsJournal of Computational Physics (JCP), 2024
Mo Zhou
Stanley Osher
Wuchen Li
379
8
0
24 Sep 2024
Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations
Neural networks for bifurcation and linear stability analysis of steady states in partial differential equationsApplied Mathematics and Computation (Appl. Math. Comput.), 2024
M. L. Shahab
Hadi Susanto
381
9
0
29 Jul 2024
Operator SVD with Neural Networks via Nested Low-Rank Approximation
Operator SVD with Neural Networks via Nested Low-Rank ApproximationInternational Conference on Machine Learning (ICML), 2024
J. Jon Ryu
Xiangxiang Xu
H. Erol
Yuheng Bu
Lizhong Zheng
G. Wornell
390
10
0
06 Feb 2024
Approximation of Solution Operators for High-dimensional PDEs
Approximation of Solution Operators for High-dimensional PDEs
Nathan Gaby
Xiaojing Ye
316
0
0
18 Jan 2024
A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional
  Nonlinear Parabolic Partial Differential Equations
A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations
E. Putri
M. L. Shahab
Mohammad Iqbal
I. Mukhlash
A. Hakam
Lutfi Mardianto
Hadi Susanto
286
1
0
20 Nov 2023
Computing excited states of molecules using normalizing flows
Computing excited states of molecules using normalizing flowsJournal of Chemical Theory and Computation (JCTC), 2023
Yahya Saleh
Álvaro Fernández Corral
Emil Vogt
Armin Iske
J. Küpper
A. Yachmenev
479
10
0
31 Aug 2023
Matrix Diagonalization as a Board Game: Teaching an Eigensolver the
  Fastest Path to Solution
Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution
Phill Romero
Manish Bhattarai
C. Negre
A. Niklasson
A. Adedoyin
265
2
0
16 Jun 2023
The Galerkin method beats Graph-Based Approaches for Spectral Algorithms
The Galerkin method beats Graph-Based Approaches for Spectral AlgorithmsInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2023
Vivien A. Cabannes
Francis R. Bach
357
4
0
01 Jun 2023
On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problemNuclear science and engineering (NSE), 2023
Yu Yang
Helin Gong
Qihong Yang
Yangtao Deng
Qiaolin He
Shiquan Zhang
DiffM
329
14
0
15 Mar 2023
A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guarantee
A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence GuaranteeSIAM Journal of Control and Optimization (SICON), 2023
Mo Zhou
Jian-Xiong Lu
361
13
0
11 Feb 2023
Neural Control of Parametric Solutions for High-dimensional Evolution
  PDEs
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Nathan Gaby
X. Ye
Haomin Zhou
395
10
0
31 Jan 2023
Neural Networks Based on Power Method and Inverse Power Method for
  Solving Linear Eigenvalue Problems
Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue ProblemsComputers and Mathematics with Applications (CMA), 2022
Qihong Yang
Yangtao Deng
Yu Yang
Qiaolin He
Shiquan Zhang
372
23
0
22 Sep 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Senwei Liang
Haizhao Yang
497
22
0
21 Jun 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic
  Equations via Gradient Descent
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient DescentNeural Information Processing Systems (NeurIPS), 2022
Yiping Lu
Jose H. Blanchet
Lexing Ying
429
11
0
15 May 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
A semigroup method for high dimensional elliptic PDEs and eigenvalue
  problems based on neural networks
A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks
Haoya Li
Lexing Ying
229
17
0
07 May 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for
  Solving High Dimensional Schrödinger Eigenvalue Problems
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue ProblemsCommunications of the American Mathematical Society (Comm. Amer. Math. Soc.), 2021
Jianfeng Lu
Yulong Lu
314
39
0
04 May 2021
Reproducing Activation Function for Deep Learning
Reproducing Activation Function for Deep LearningCommunications in Mathematical Sciences (CMS), 2021
Senwei Liang
Liyao Lyu
Chunmei Wang
Haizhao Yang
365
28
0
13 Jan 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving
  High Dimensional Elliptic Equations
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
Jianfeng Lu
Yulong Lu
Min Wang
319
37
0
05 Jan 2021
Recurrent Neural Networks for Stochastic Control Problems with Delay
Recurrent Neural Networks for Stochastic Control Problems with DelayMCSS. Mathematics of Control, Signals and Systems (MCSS), 2021
Jiequn Han
Ruimeng Hu
234
22
0
05 Jan 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
Convergence to the fixed-node limit in deep variational Monte Carlo
Convergence to the fixed-node limit in deep variational Monte CarloJournal of Chemical Physics (JCP), 2020
Zeno Schätzle
J. Hermann
Frank Noé
226
23
0
11 Oct 2020
Convergence of Deep Fictitious Play for Stochastic Differential Games
Convergence of Deep Fictitious Play for Stochastic Differential Games
Jiequn Han
Ruimeng Hu
Jihao Long
447
22
0
12 Aug 2020
Deep neural network approximation for high-dimensional elliptic PDEs
  with boundary conditions
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditionsIMA Journal of Numerical Analysis (IMA J. Numer. Anal.), 2020
Philipp Grohs
L. Herrmann
334
58
0
10 Jul 2020
Improving neural network predictions of material properties with limited
  data using transfer learning
Improving neural network predictions of material properties with limited data using transfer learning
Schuyler Krawczuk
D. Venturi
AI4CE
201
4
0
29 Jun 2020
Convergence of the Deep BSDE Method for Coupled FBSDEs
Convergence of the Deep BSDE Method for Coupled FBSDEs
Jiequn Han
Jihao Long
277
183
0
03 Nov 2018
1
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