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Fourier Neural Operator for Parametric Partial Differential Equations

18 October 2020

Zong-Yi Li

Nikola B. Kovachki

Kamyar Azizzadenesheli

Papers citing "Fourier Neural Operator for Parametric Partial Differential Equations"

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Title
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Guided Diffusion Sampling on Function Spaces with Applications to PDEs Jiachen Yao Abbas Mammadov Julius Berner Gavin Kerrigan Jong Chul Ye Kamyar Azizzadenesheli A. Anandkumar DiffM 94 3 0 22 May 2025
Consistent World Models via Foresight Diffusion Yu Zhang Xingzhuo Guo Haoran Xu Mingsheng Long 57 0 0 22 May 2025
FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model Jiahuan Long Wenzhe Zhang Ning Wang Tingsong Jiang Wen Yao Mamba AI4CE 69 0 0 21 May 2025
Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators Luca Pellegrini Massimiliano Ghiotto Edoardo Centofanti Luca Franco Pavarino 76 0 0 20 May 2025
Net-Zero: A Comparative Study on Neural Network Design for Climate-Economic PDEs Under Uncertainty Carlos Rodriguez-Pardo Louis Daumas Leonardo Chiani Massimo Tavoni 42 0 0 19 May 2025
Neural Functional: Learning Function to Scalar Maps for Neural PDE Surrogates Anthony Zhou Amir Barati Farimani AI4CE 66 0 0 19 May 2025
Multi-Level Monte Carlo Training of Neural Operators James Rowbottom Stefania Fresca Pietro Lio Carola-Bibiane Schönlieb Nicolas Boullé AI4CE 111 1 0 19 May 2025
Engineering application of physics-informed neural networks for Saint-Venant torsion Su Yeong Jo Sanghyeon Park Seungchan Ko Jongcheon Park Hosung Kim Sangseung Lee Joongoo Jeon PINN 62 0 0 18 May 2025
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Taniya Kapoor Abhishek Chandra Anastasios Stamou Stephen J Roberts 74 1 0 18 May 2025
LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE Siwen Zhang Xizeng Zhao Zhengzhi Deng Zhaoyuan Huang Gang Tao Nuo Xu Zhouteng Ye 68 0 0 18 May 2025
S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation Junlang Huang Hao Chen Li Luo Yong Cai Lexin Zhang Tianhao Ma Yitian Zhang Zhong Guan 86 0 0 17 May 2025
Redefining Neural Operators in $d+1$ Dimensions Haoze Song Zhihao Li Xiaobo Zhang Zecheng Gan Zhilu Lai Wei Wang 53 0 0 17 May 2025
GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations Xi Han Jingwei Zhang Dimitris Samaras Fei Hou Hong Qin AI4CE 109 0 0 17 May 2025
Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning Ananyae Kumar Bhartari Vinayak Vinayak Vivek B Shenoy AI4CE 210 0 0 16 May 2025
Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models Congcong Zhu Xiaoyan Xu Jiayue Han Jingrun Chen OOD AI4CE 149 0 0 16 May 2025
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data Lothar Heimbach Sebastian Kaltenbach Petr Karnakov Francis J. Alexander Petros Koumoutsakos AI4CE 128 0 0 16 May 2025
A Physics-Informed Convolutional Long Short Term Memory Statistical Model for Fluid Thermodynamics Simulations Luca Menicali Andrew Grace David H. Richter Stefano Castruccio AI4CE 83 0 0 16 May 2025
Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning Yuanzhao Zhang William Gilpin AI4TS 76 0 0 16 May 2025
On the definition and importance of interpretability in scientific machine learning Conor Rowan Alireza Doostan AI4CE 89 0 0 16 May 2025
Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations Victor Zheleznov Stefan Bilbao Alec Wright Simon King 67 0 0 15 May 2025
Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations Giovanni Catalani Jean Fesquet Xavier Bertrand Frédéric Tost Michaël Bauerheim Joseph Morlier AI4CE 60 0 0 14 May 2025
Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Abdolmehdi Behroozi Chaopeng Shen and Daniel Kifer AI4CE 120 0 0 13 May 2025
Learning cardiac activation and repolarization times with operator learning Edoardo Centofanti Giovanni Ziarelli N. Parolini Simone Scacchi M. Verani Luca Franco Pavarino AI4CE 60 0 0 13 May 2025
Non-Stationary Time Series Forecasting Based on Fourier Analysis and Cross Attention Mechanism Yuqi Xiong Yang Wen AI4TS 50 0 0 11 May 2025
FreqMoE: Dynamic Frequency Enhancement for Neural PDE Solvers Tianyu Chen Haoyi Zhou Yunshui Li Hao Wang Zhenru Zhang Tianchen Zhu Shanghang Zhang Junlong Li 95 0 0 11 May 2025
Universal Approximation Theorem for Deep Q-Learning via FBSDE System Qian Qi 82 0 0 09 May 2025
Learning dynamically inspired invariant subspaces for Koopman and transfer operator approximation Gary Froyland Kevin Kühl 86 0 0 08 May 2025
SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimation Wenqing Peng Zhi-Song Liu Michael Boy 110 0 0 08 May 2025
SetONet: A Deep Set-based Operator Network for Solving PDEs with permutation invariant variable input sampling Stepan Tretiakov Xingjian Li Krishna Kumar 72 0 0 07 May 2025
Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equations Vincent Souveton Sébastien Terrana 96 0 0 07 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 423 0 0 06 May 2025
Predicting The Evolution of Interfaces with Fourier Neural Operators Paolo Guida William L. Roberts AI4CE 123 0 0 05 May 2025
Exploring Design Choices for Autoregressive Deep Learning Climate Models Florian Gallusser Simon Hentschel Anna Krause Andreas Hotho AI4Cl 112 0 0 05 May 2025
Enabling Local Neural Operators to perform Equation-Free System-Level Analysis Gianluca Fabiani H. Vandecasteele S. Goswami Constantinos Siettos Ioannis G. Kevrekidis 453 1 0 05 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 97 1 0 03 May 2025
A Physics-preserved Transfer Learning Method for Differential Equations Hao-Ran Yang Chuan-Xian Ren 442 0 0 02 May 2025
Learning and Transferring Physical Models through Derivatives Alessandro Trenta Andrea Cossu Davide Bacciu AI4CE 78 0 0 02 May 2025
Interpretable Spatial-Temporal Fusion Transformers: Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs Shuwen Sun Lihong Feng P. Benner 81 0 0 01 May 2025
Data-driven operator learning for energy-efficient building control Yuexin Bian Yuanyuan Shi AI4CE 126 0 0 30 Apr 2025
Evaluation and Verification of Physics-Informed Neural Models of the Grad-Shafranov Equation Fauzan Nazranda Rizqan Matthew Hole Charles Gretton 117 0 0 29 Apr 2025
FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation Jae Yong Lee Gwang Jae Jung Byung Chan Lim Hyung Ju Hwang 78 0 0 29 Apr 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
HJRNO: Hamilton-Jacobi Reachability with Neural Operators Yankai Li Mo Chen 87 0 0 28 Apr 2025
Deep Physics Prior for First Order Inverse Optimization Haoyu Yang Kamyar Azizzadenesheli Haoxing Ren PINN AI4CE 171 0 0 28 Apr 2025
Geometry-Informed Neural Operator Transformer Qibang Liu Vincient Zhong Hadi Meidani Diab Abueidda S. Koric Philippe Geubelle AI4CE 91 1 0 28 Apr 2025
Optimizing Hard Thresholding for Sparse Model Discovery Derek W. Jollie Scott G. McCalla 91 0 0 28 Apr 2025
Neural operators struggle to learn complex PDEs in pedestrian mobility: Hughes model case study Prajwal Chauhan Salah Eddine Choutri Mohamed Ghattassi Nader Masmoudi Saif Eddin Jabari 88 0 0 25 Apr 2025