Learning Neural PDE Solvers with Convergence Guarantees

4 June 2019

Papers citing "Learning Neural PDE Solvers with Convergence Guarantees"

28 / 28 papers shown

Title
DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction Rudy Morel Jiequn Han Edouard Oyallon AI4CE 56 0 0 28 Apr 2025
Unsupervised Representation Learning from Sparse Transformation Analysis Yue Song Thomas Anderson Keller Yisong Yue Pietro Perona Max Welling DRL 31 0 0 07 Oct 2024
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations N. McGreivy Ammar Hakim AI4CE 34 43 0 09 Jul 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 40 5 0 27 Feb 2024
Neural Multigrid Architectures V. Fanaskov 8 3 0 08 Feb 2024
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Mingtao Xia Xiangting Li Qijing Shen Tom Chou 19 0 0 28 Sep 2023
Invariant preservation in machine learned PDE solvers via error correction N. McGreivy Ammar Hakim AI4CE PINN 29 8 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 23 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 23 8 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 29 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 34 2 0 06 Feb 2023
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 52 10 0 21 Oct 2022
Towards Multi-spatiotemporal-scale Generalized PDE Modeling Jayesh K. Gupta Johannes Brandstetter AI4CE 61 119 0 30 Sep 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 42 144 0 26 May 2022
Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations Maximilian Mueller Robin Greif Frank Jenko Nils Thuerey 24 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 36 8 0 01 Mar 2022
Learning To Estimate Regions Of Attraction Of Autonomous Dynamical Systems Using Physics-Informed Neural Networks Cody Scharzenberger Joe Hays 40 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 40 22 0 28 Sep 2021
Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Network Ekhi Ajuria Illarramendi M. Bauerheim B. Cuenot 33 19 0 20 Sep 2021
Cell-average based neural network method for hyperbolic and parabolic partial differential equations Changxin Qiu Jue Yan 16 10 0 02 Jul 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 8 22 0 07 May 2021
Learning optimal multigrid smoothers via neural networks Ru Huang Ruipeng Li Yuanzhe Xi AI4CE 18 27 0 24 Feb 2021
Measure Anatomical Thickness from Cardiac MRI with Deep Neural Networks Qiaoying Huang Eric Z. Chen Hanchao Yu Yimo Guo Terrence Chen Dimitris N. Metaxas Shanhui Sun 14 1 0 25 Aug 2020
DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization Rishikesh Ranade C. Hill Jay Pathak AI4CE 54 123 0 17 May 2020
Enhancement of shock-capturing methods via machine learning Ben Stevens T. Colonius 12 46 0 06 Feb 2020
FEA-Net: A Physics-guided Data-driven Model for Efficient Mechanical Response Prediction Houpu Yao Yi Gao Yongming Liu AI4CE 61 66 0 31 Jan 2020
Learning to Control PDEs with Differentiable Physics Philipp Holl V. Koltun Nils Thuerey AI4CE PINN 44 185 0 21 Jan 2020
Variational training of neural network approximations of solution maps for physical models Yingzhou Li Jianfeng Lu Anqi Mao GAN 19 35 0 07 May 2019