Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

10 February 2023

Papers citing "Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation"

49 / 49 papers shown

Title
Spectral-inspired Neural Operator for Data-efficient PDE Simulation in Physics-agnostic Regimes Han Wan Rui Zhang Hao Sun AI4CE 50 0 0 27 May 2025
PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Han Wan Rui Zhang Qi Wang Yang Liu Hao Sun PINN 64 1 0 03 May 2025
HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork Jae Yong Lee S. Cho H. Hwang 53 23 0 26 Dec 2023
Deciphering and integrating invariants for neural operator learning with various physical mechanisms Rui Zhang Qi Meng Zhi-Ming Ma AI4CE 71 9 0 24 Nov 2023
Physics informed WNO N. N. Tapas Tripura S. Chakraborty 63 30 0 12 Feb 2023
Can Physics-Informed Neural Networks beat the Finite Element Method? T. G. Grossmann Urszula Julia Komorowska J. Latz Carola-Bibiane Schönlieb PINN AI4CE 83 90 0 08 Feb 2023
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 58 34 0 06 Dec 2022
Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty Luning Sun Daniel Zhengyu Huang Hao Sun Jian-Xun Wang 59 10 0 14 Oct 2022
Transformer Meets Boundary Value Inverse Problems Ruchi Guo Shuhao Cao Long Chen MedIm 65 22 0 29 Sep 2022
FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators Thorsten Kurth Shashank Subramanian P. Harrington Jaideep Pathak Morteza Mardani D. Hall Andrea Miele K. Kashinath Anima Anandkumar AI4Cl 81 187 0 08 Aug 2022
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries Zong-Yi Li Daniel Zhengyu Huang Burigede Liu Anima Anandkumar AI4CE 169 268 0 11 Jul 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 55 19 0 21 Jun 2022
Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equations Rui Zhang Tailin Wu Qi Meng Yue Wang Rongchan Zhu Bingguang Chen Zhi-Ming Ma Tie-Yan Liu 44 15 0 20 Jun 2022
NOMAD: Nonlinear Manifold Decoders for Operator Learning Jacob H. Seidman Georgios Kissas P. Perdikaris George J. Pappas AI4CE 72 75 0 07 Jun 2022
Learning to Solve PDE-constrained Inverse Problems with Graph Networks Qingqing Zhao David B. Lindell Gordon Wetzstein AI4CE 80 40 0 01 Jun 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 100 162 0 26 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 69 8 0 15 May 2022
SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability Simone Venturi T. Casey 65 38 0 27 Apr 2022
U-NO: U-shaped Neural Operators Md Ashiqur Rahman Zachary E. Ross Kamyar Azizzadenesheli AI4CE 107 144 0 23 Apr 2022
Message Passing Neural PDE Solvers Johannes Brandstetter Daniel E. Worrall Max Welling AI4CE 76 282 0 07 Feb 2022
Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients Rohan Sawhney Dario Seyb Wojciech Jarosz Keenan Crane 58 33 0 31 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 60 29 0 07 Dec 2021
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 71 155 0 27 Nov 2021
Composing Partial Differential Equations with Physics-Aware Neural Networks Matthias Karlbauer T. Praditia S. Otte S. Oladyshkin Wolfgang Nowak Martin Volker Butz AI4CE 73 20 0 23 Nov 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 119 414 0 06 Nov 2021
Improved architectures and training algorithms for deep operator networks Sizhuang He Hanwen Wang P. Perdikaris AI4CE 84 107 0 04 Oct 2021
Multiwavelet-based Operator Learning for Differential Equations Gaurav Gupta Xiongye Xiao P. Bogdan 178 217 0 28 Sep 2021
CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries Yi-Zhou Wang Jia Sun Wei Li Zaiyuan Lu Yinghua Liu 88 40 0 25 Sep 2021
Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs Nils Wandel Michael Weinmann Michael Neidlin Reinhard Klein AI4CE 73 62 0 15 Sep 2021
Characterizing possible failure modes in physics-informed neural networks Aditi S. Krishnapriyan A. Gholami Shandian Zhe Robert M. Kirby Michael W. Mahoney PINN AI4CE 111 640 0 02 Sep 2021
Towards Out-Of-Distribution Generalization: A Survey Jiashuo Liu Zheyan Shen Yue He Xingxuan Zhang Renzhe Xu Han Yu Peng Cui CML OOD 147 533 0 31 Aug 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 69 245 0 31 May 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 95 699 0 19 Mar 2021
Solving high-dimensional parabolic PDEs using the tensor train format Lorenz Richter Leon Sallandt Nikolas Nusken 63 50 0 23 Feb 2021
Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs Jie Bu Anuj Karpatne 58 49 0 20 Jan 2021
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method Sebastian K. Mitusch S. Funke M. Kuchta AI4CE 106 97 0 04 Jan 2021
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D Nils Wandel Michael Weinmann Reinhard Klein AI4CE 66 51 0 22 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 497 2,414 0 18 Oct 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 135 909 0 28 Jul 2020
Physics-informed learning of governing equations from scarce data Zhao Chen Yang Liu Hao Sun PINN AI4CE 62 394 0 05 May 2020
Neural Operator: Graph Kernel Network for Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar 196 736 0 07 Mar 2020
Learning to Simulate Complex Physics with Graph Networks Alvaro Sanchez-Gonzalez Jonathan Godwin Tobias Pfaff Rex Ying J. Leskovec Peter W. Battaglia PINN AI4CE 139 1,091 0 21 Feb 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 61 50 0 17 Jan 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 68 264 0 12 Jan 2020
PyTorch: An Imperative Style, High-Performance Deep Learning Library Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 493 42,449 0 03 Dec 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 245 2,131 0 08 Oct 2019
Deep neural network solution of the electronic Schrödinger equation J. Hermann Zeno Schätzle Frank Noé 208 456 0 16 Sep 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 198 1,379 0 27 Aug 2019
U-Net: Convolutional Networks for Biomedical Image Segmentation Olaf Ronneberger Philipp Fischer Thomas Brox SSeg 3DV 1.8K 77,196 0 18 May 2015