The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

30 September 2017

Papers citing "The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems"

50 / 231 papers shown

Title
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks Zihan Shao Konstantin Pieper Xiaochuan Tian 31 0 0 12 May 2025
Physics-informed solution reconstruction in elasticity and heat transfer using the explicit constraint force method Conor Rowan K. Maute Alireza Doostan AI4CE 53 0 0 08 May 2025
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs Sidharth S. Menon Ameya D. Jagtap PINN 214 0 0 06 May 2025
Integration Matters for Learning PDEs with Backwards SDEs Sungje Park Stephen Tu PINN 65 0 0 02 May 2025
PODNO: Proper Orthogonal Decomposition Neural Operators Zilan Cheng Zhongjian Wang Li-Lian Wang Mejdi Azaiez 36 0 0 25 Apr 2025
Reliable and Efficient Inverse Analysis using Physics-Informed Neural Networks with Distance Functions and Adaptive Weight Tuning Shota Deguchi Mitsuteru Asai PINN AI4CE 81 0 0 25 Apr 2025
From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs Rohan Bhatnagar Ling Liang Krish Patel Haizhao Yang 36 0 0 13 Mar 2025
Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble Zongren Zou Zhicheng Wang George Karniadakis PINN AI4CE 73 2 0 08 Mar 2025
Verification and Validation for Trustworthy Scientific Machine Learning John D. Jakeman Lorena A. Barba J. Martins Thomas O'Leary-Roseberry AI4CE 62 0 0 21 Feb 2025
Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks A. Celaya Yimo Wang David T. Fuentes Beatrice Riviere 41 0 0 12 Feb 2025
DGNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling Yaohua Zang P. Koutsourelakis AI4CE 54 1 0 10 Feb 2025
Learn Sharp Interface Solution by Homotopy Dynamics Chuqi Chen Yahong Yang Yang Xiang Wenrui Hao ODL 65 1 0 01 Feb 2025
Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths Yueyang Wang Kejun Tang Xili Wang Xiaoliang Wan Weiqing Ren Chao Yang 40 0 0 28 Jan 2025
A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting Kasper Bågmark Adam Andersson S. Larsson Filip Rydin 82 0 0 20 Jan 2025
Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants N. Sukumar Amit Acharya 86 2 0 02 Dec 2024
Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators Zekun Shi Zheyuan Hu Min Lin Kenji Kawaguchi 215 6 0 27 Nov 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 40 10 0 02 Oct 2024
Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Theory Perspective Taeyoung Kim Myungjoo Kang 35 0 0 04 Aug 2024
Equidistribution-based training of Free Knot Splines and ReLU Neural Networks Simone Appella S. Arridge Chris Budd Teo Deveney L. Kreusser 38 0 0 02 Jul 2024
Efficient Shallow Ritz Method For 1D Diffusion-Reaction Problems Zhiqiang Cai Anastassia Doktorova Robert D. Falgout César Herrera 21 0 0 01 Jul 2024
Solving Poisson Equations using Neural Walk-on-Spheres Hong Chul Nam Julius Berner Anima Anandkumar 39 3 0 05 Jun 2024
Astral: training physics-informed neural networks with error majorants V. Fanaskov Tianchi Yu Alexander Rudikov Ivan Oseledets 41 1 0 04 Jun 2024
Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media Matthaios Chatzopoulos P. Koutsourelakis AI4CE 41 3 0 29 May 2024
Physics informed cell representations for variational formulation of multiscale problems Yuxiang Gao Soheil Kolouri R. Duddu AI4CE 37 0 0 27 May 2024
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations Chuqi Chen Yahong Yang Yang Xiang Wenrui Hao 26 2 0 23 May 2024
Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing Ning Liu Xuxiao Li M. Rajanna E. Reutzel Brady A Sawyer Prahalada Rao Jim Lua Nam Phan Yue Yu AI4CE 48 8 0 13 May 2024
Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks R. Mattey Susanta Ghosh AI4CE 48 1 0 09 May 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 45 7 0 08 May 2024
A score-based particle method for homogeneous Landau equation Yan Huang Li Wang OT 55 5 0 08 May 2024
KAN: Kolmogorov-Arnold Networks Ziming Liu Yixuan Wang Sachin Vaidya Fabian Ruehle James Halverson Marin Soljacic Thomas Y. Hou Max Tegmark 98 485 0 30 Apr 2024
Accurate adaptive deep learning method for solving elliptic problems Jingyong Ying Yaqi Xie Jiao Li Hongqiao Wang 40 1 0 29 Apr 2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations Hongyan Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 35 2 0 04 Mar 2024
A time-stepping deep gradient flow method for option pricing in (rough) diffusion models A. Papapantoleon Jasper Rou 24 2 0 01 Mar 2024
Learning solution operators of PDEs defined on varying domains via MIONet Shanshan Xiao Pengzhan Jin Yifa Tang 55 3 0 23 Feb 2024
DeepLag: Discovering Deep Lagrangian Dynamics for Intuitive Fluid Prediction Qilong Ma Haixu Wu Lanxiang Xing Jianmin Wang Mingsheng Long AI4CE 34 0 0 04 Feb 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models E. Georgoulis A. Papapantoleon Costas Smaragdakis 26 6 0 12 Jan 2024
Generating synthetic data for neural operators Erisa Hasani Rachel A. Ward AI4CE 67 8 0 04 Jan 2024
Machine learning and domain decomposition methods -- a survey A. Klawonn M. Lanser J. Weber AI4CE 24 7 0 21 Dec 2023
Unsupervised Random Quantum Networks for PDEs Josh Dees Antoine Jacquier Sylvain Laizet 24 2 0 21 Dec 2023
Dynamically configured physics-informed neural network in topology optimization applications Ji-Cheng Yin Ziming Wen Shuhao Li Yaya Zhang Hu Wang AI4CE PINN 44 4 0 12 Dec 2023
Statistical Spatially Inhomogeneous Diffusion Inference Yinuo Ren Yiping Lu Lexing Ying Grant M. Rotskoff 22 2 0 10 Dec 2023
GIT-Net: Generalized Integral Transform for Operator Learning Chao Wang Alexandre H. Thiery AI4CE 37 0 0 05 Dec 2023
Adaptive importance sampling for Deep Ritz Xiaoliang Wan Tao Zhou Yuancheng Zhou 29 2 0 26 Oct 2023
Learning to Predict Structural Vibrations J. V. Delden Julius Schultz Christopher Blech Sabine C. Langer Timo Luddecke AI4CE 29 1 0 09 Oct 2023
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp Dibyakanti Kumar Anirbit Mukherjee 31 2 0 08 Oct 2023
Neural Stochastic Screened Poisson Reconstruction Silvia Sellán Alec Jacobson 3DV 35 6 0 21 Sep 2023
Latent assimilation with implicit neural representations for unknown dynamics Zhuoyuan Li Bin Dong Pingwen Zhang AI4CE 24 3 0 18 Sep 2023
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation Yuesheng Xu Taishan Zeng AI4CE 32 4 0 14 Sep 2023
Solving multiscale elliptic problems by sparse radial basis function neural networks Zhiwen Wang Minxin Chen Jingrun Chen 52 15 0 01 Sep 2023