Learning Neural PDE Solvers with Convergence Guarantees

4 June 2019

Papers citing "Learning Neural PDE Solvers with Convergence Guarantees"

50 / 78 papers shown

Title
Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators Ze Cheng Zhuoyu Li Xiaoqiang Wang Jianing Huang Zhizhou Zhang Zhongkai Hao Hang Su 15 0 0 16 Jun 2025
Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates Yunfei Huang David S. Greenberg AI4CE 28 0 0 05 Jun 2025
DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction Rudy Morel Jiequn Han Edouard Oyallon AI4CE 94 1 0 28 Apr 2025
Using Parametric PINNs for Predicting Internal and External Turbulent Flows Shinjan Ghosh Amit Chakraborty Georgia Olympia Brikis Biswadip Dey 34 1 0 24 Oct 2024
Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods Lise Le Boudec Emmanuel de Bézenac Louis Serrano Ramon Daniel Regueiro-Espino Yuan Yin Patrick Gallinari AI4CE 92 2 0 09 Oct 2024
Unsupervised Representation Learning from Sparse Transformation Analysis Yue Song Thomas Anderson Keller Yisong Yue Pietro Perona Max Welling DRL 71 0 0 07 Oct 2024
UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs Xi Han Fei Hou Hong Qin AI4CE 70 2 0 09 Aug 2024
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations N. McGreivy Ammar Hakim AI4CE 113 56 0 09 Jul 2024
ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations Vladislav Trifonov Alexander Rudikov Oleg Iliev Ivan Oseledets Ekaterina Muravleva Ekaterina Muravleva DiffM AI4CE 69 0 0 07 Jun 2024
Accelerating Legacy Numerical Solvers by Non-intrusive Gradient-based Meta-solving S. Arisaka Qianxiao Li 79 0 0 05 May 2024
Stabilizing Backpropagation Through Time to Learn Complex Physics Patrick Schnell Nils Thuerey 105 2 0 03 May 2024
UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation Junhong Shen Tanya Marwah Ameet Talwalkar AI4CE 93 6 0 11 Mar 2024
Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations Zijie Li Saurabh Patil Francis Ogoke Dule Shu Wilson Zhen Michael Schneier John R. Buchanan A. Farimani AI4CE 80 5 0 27 Feb 2024
PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equations Shiyi Qi Zenglin Xu Yiduo Li Liangjiang Wen Qingsong Wen Qifan Wang Yuan Qi AI4TS AI4CE 93 0 0 25 Feb 2024
Neural Multigrid Architectures V. Fanaskov 37 3 0 08 Feb 2024
Accelerating PDE Data Generation via Differential Operator Action in Solution Space Huanshuo Dong Hong Wang Haoyang Liu Jian Luo Jie Wang AI4CE 58 2 0 04 Feb 2024
Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling Hong Wang Zhongkai Hao Jie Wang Zijie Geng Zhen Wang Bin Li Fengli Wu 45 3 0 17 Jan 2024
Deep Equilibrium Based Neural Operators for Steady-State PDEs Tanya Marwah Ashwini Pokle J. Zico Kolter Zachary Chase Lipton Jianfeng Lu Andrej Risteski 88 8 0 30 Nov 2023
Interpretable Neural PDE Solvers using Symbolic Frameworks Yolanne Yi Ran Lee AI4CE 76 0 0 31 Oct 2023
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Mingtao Xia Xiangting Li Qijing Shen Tom Chou 38 0 0 28 Sep 2023
Deep Learning in Deterministic Computational Mechanics L. Herrmann Stefan Kollmannsberger AI4CE PINN 114 0 0 27 Sep 2023
Flow Factorized Representation Learning Yue Song Thomas Anderson Keller N. Sebe Max Welling DRL OOD 125 3 0 22 Sep 2023
PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers Phillip Lippe Bastiaan S. Veeling P. Perdikaris Richard Turner Johannes Brandstetter DiffM AI4CE 129 96 0 10 Aug 2023
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers Bar Lerer Ido Ben-Yair Eran Treister AI4CE 62 3 0 30 Jun 2023
Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries Ihda Chaerony Siffa M. Becker K. Weltmann J. Trieschmann 62 2 0 13 Jun 2023
RANS-PINN based Simulation Surrogates for Predicting Turbulent Flows Shinjan Ghosh Amit Chakraborty Georgia Olympia Brikis Biswadip Dey PINN AI4CE 56 5 0 09 Jun 2023
Learning Neural PDE Solvers with Parameter-Guided Channel Attention M. Takamoto Francesco Alesiani Mathias Niepert 106 26 0 27 Apr 2023
Latent Traversals in Generative Models as Potential Flows Yue Song Andy Keller N. Sebe Max Welling DRL 114 11 0 25 Apr 2023
Invariant preservation in machine learned PDE solvers via error correction N. McGreivy Ammar Hakim AI4CE PINN 79 9 0 28 Mar 2023
Neural Partial Differential Equations with Functional Convolution Z. Wu Xingzhe He Yijun Li Cheng Yang Rui Liu S. Xiong Bo Zhu 61 1 0 10 Mar 2023
NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition Xinquan Huang Wenlei Shi Qi Meng Yue Wang Xiaotian Gao Jia Zhang Tie-Yan Liu AI4CE 68 10 0 20 Feb 2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations Arnulf Jentzen Adrian Riekert Philippe von Wurstemberger 74 1 0 07 Feb 2023
An Implicit GNN Solver for Poisson-like problems Matthieu Nastorg M. Bucci T. Faney J. Gratien Guillaume Charpiat Marc Schoenauer AI4CE 95 2 0 06 Feb 2023
Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations Yemo Li Yiwen Pang Bin Shan AI4CE 73 5 0 08 Dec 2022
Meta-PDE: Learning to Solve PDEs Quickly Without a Mesh Tian Qin Alex Beatson Deniz Oktay N. McGreivy Ryan P. Adams AI4CE 76 10 0 03 Nov 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 78 10 0 21 Oct 2022
Towards Multi-spatiotemporal-scale Generalized PDE Modeling Jayesh K. Gupta Johannes Brandstetter AI4CE 137 136 0 30 Sep 2022
Clifford Neural Layers for PDE Modeling Johannes Brandstetter Rianne van den Berg Max Welling Jayesh K. Gupta AI4CE 122 90 0 08 Sep 2022
Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks Winfried Lotzsch Simon Ohler Johannes Otterbach AI4CE 82 19 0 28 Jun 2022
LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data Xinquan Huang Wenlei Shi Xiaotian Gao Xinran Wei Jia Zhang Jiang Bian Mao Yang Tie-Yan Liu PINN 95 11 0 19 Jun 2022
Principled Acceleration of Iterative Numerical Methods Using Machine Learning S. Arisaka Qianxiao Li 108 6 0 17 Jun 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 117 172 0 26 May 2022
A Deep Conjugate Direction Method for Iteratively Solving Linear Systems Ayano Kaneda Osman Akar Jingyu Chen Victoria Kala David Hyde Joseph Teran 81 12 0 22 May 2022
Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations Maximilian Mueller Robin Greif Frank Jenko Nils Thuerey 74 3 0 02 May 2022
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space Juncai He R. Tsai Rachel A. Ward 82 9 0 01 Mar 2022
Lie Point Symmetry Data Augmentation for Neural PDE Solvers Johannes Brandstetter Max Welling Daniel E. Worrall AI4CE 100 64 0 15 Feb 2022
Message Passing Neural PDE Solvers Johannes Brandstetter Daniel E. Worrall Max Welling AI4CE 128 288 0 07 Feb 2022
An Interpretive Constrained Linear Model for ResNet and MgNet Juncai He Jinchao Xu Lian Zhang Jianqing Zhu 77 18 0 14 Dec 2021
Learning To Estimate Regions Of Attraction Of Autonomous Dynamical Systems Using Physics-Informed Neural Networks Cody Scharzenberger Joe Hays 74 3 0 18 Nov 2021
Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning Ziming Liu Yunyue Chen Yuanqi Du Max Tegmark PINN AI4CE 91 22 0 28 Sep 2021