DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data

13 August 2019

Papers citing "DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data"

37 / 37 papers shown

Title
Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models Congcong Zhu Xiaoyan Xu Jiayue Han Jingrun Chen OOD AI4CE 41 0 0 16 May 2025
Generative Discovery of Partial Differential Equations by Learning from Math Handbooks Hao Xu Y. Chen Rui Cao Tianning Tang Mengge Du Jiacheng Li Adrian H. Callaghan Dongxiao Zhang 29 0 0 09 May 2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis Yasamin Jalalian Juan Felipe Osorio Ramirez Alexander W. Hsu Bamdad Hosseini H. Owhadi 46 0 0 02 Mar 2025
Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression Ding Wang Yuntian Chen Shiyi Chen 40 0 0 02 Jun 2024
An invariance constrained deep learning network for PDE discovery Chao Chen Hui Li Xiaowei Jin PINN 17 1 0 06 Feb 2024
Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework Dashan Zhang Yuntian Chen Shiyi Chen AI4CE 32 2 0 07 Nov 2023
Deep Learning based Spatially Dependent Acoustical Properties Recovery Ruixian Liu Peter Gerstoft 22 0 0 17 Oct 2023
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology Qingsong Xu Yilei Shi Jonathan Bamber Ye Tuo Ralf Ludwig Xiao Xiang Zhu AI4CE 20 10 0 08 Oct 2023
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations Mingtao Xia Xiangting Li Qijing Shen Tom Chou 19 0 0 28 Sep 2023
Physics-constrained robust learning of open-form partial differential equations from limited and noisy data Mengge Du Yuntian Chen Longfeng Nie Siyu Lou Dong-juan Zhang AI4CE 31 7 0 14 Sep 2023
PDE Discovery for Soft Sensors Using Coupled Physics-Informed Neural Network with Akaike's Information Criterion Aina Wang Pan Qin Ximing Sun 11 0 0 11 Aug 2023
Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO) O. Ovadia Vivek Oommen Adar Kahana Ahmad Peyvan Eli Turkel George Karniadakis AI4CE 45 13 0 18 Jul 2023
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences E. Celledoni James Jackaman Davide Murari B. Owren 35 2 0 01 May 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 35 5 0 26 Apr 2023
WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming Mengyi Tang Wenjing Liao R. Kuske S. Kang 9 16 0 06 Nov 2022
DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learning Mengge Du Yuntian Chen Dong-juan Zhang 33 0 0 04 Oct 2022
Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion Hao Xu Junsheng Zeng Dongxiao Zhang DiffM 25 19 0 05 Aug 2022
D-CIPHER: Discovery of Closed-form Partial Differential Equations Krzysztof Kacprzyk Zhaozhi Qian M. Schaar AI4CE 30 1 0 21 Jun 2022
Discovering Governing Equations by Machine Learning implemented with Invariance Chao Chen Xiaowei Jin Hui Li PINN AI4CE 14 1 0 29 Mar 2022
Multigoal-oriented dual-weighted-residual error estimation using deep neural networks Ayan Chakraborty T. Wick X. Zhuang Timon Rabczuk 22 8 0 21 Dec 2021
Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning Xiaoqian Chen B. Nadiga I. Timofeyev 15 5 0 16 Dec 2021
PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning R. Stephany Christopher Earls DiffM AIMat 14 29 0 01 Nov 2021
ST-PCNN: Spatio-Temporal Physics-Coupled Neural Networks for Dynamics Forecasting Yu Huang James Li Min Shi H. Zhuang Xingquan Zhu Laurent Chérubin James H. VanZwieten Yufei Tang AI4CE PINN 23 6 0 12 Aug 2021
Physics-Coupled Spatio-Temporal Active Learning for Dynamical Systems Yu Huang Yufei Tang Xingquan Zhu Min Shi Ali Muhamed Ali H. Zhuang Laurent Chérubin AI4CE 22 3 0 11 Aug 2021
Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data Christophe Bonneville Christopher Earls 10 14 0 05 Aug 2021
Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations Zhiming Zhang Yongming Liu 6 11 0 08 Jul 2021
Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE) Yuntian Chen Yingtao Luo Qiang Liu Hao Xu Dongxiao Zhang AI4CE 25 56 0 09 Jun 2021
Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations Yingtao Luo Qiang Liu Yuntian Chen Wenbo Hu Tian Tian Jun Zhu DiffM 53 4 0 02 Jun 2021
Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data Junsheng Zeng Hao Xu Yuntian Chen Dongxiao Zhang 25 3 0 31 May 2021
Robust discovery of partial differential equations in complex situations Hao Xu Dongxiao Zhang AI4CE 17 28 0 31 May 2021
Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data Hao Xu Dongxiao Zhang Nanzhe Wang 27 33 0 24 Nov 2020
Data-driven Identification of 2D Partial Differential Equations using extracted physical features Kazem Meidani A. Farimani 21 17 0 20 Oct 2020
Learning continuous-time PDEs from sparse data with graph neural networks V. Iakovlev Markus Heinonen Harri Lähdesmäki AI4CE 19 68 0 16 Jun 2020
Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Data Hao Xu Dongxiao Zhang Junsheng Zeng 25 57 0 16 May 2020
The role of surrogate models in the development of digital twins of dynamic systems S. Chakraborty S. Adhikari R. Ganguli SyDa 14 103 0 25 Jan 2020
DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm Hao Xu Haibin Chang Dongxiao Zhang AI4CE 25 87 0 21 Jan 2020
Learning Partial Differential Equations from Data Using Neural Networks Ali Hasan João M. Pereira Robert J. Ravier Sina Farsiu Vahid Tarokh 11 17 0 22 Oct 2019