Data-driven discovery of PDEs in complex datasets

31 August 2018

Papers citing "Data-driven discovery of PDEs in complex datasets"

50 / 58 papers shown

Title
Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models Congcong Zhu Xiaoyan Xu Jiayue Han Jingrun Chen OOD AI4CE 133 0 0 16 May 2025
Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks D. Anton Jendrik-Alexander Tröger Henning Wessels Ulrich Römer Alexander Henkes Stefan Hartmann AI4CE 93 4 0 28 May 2024
GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations Ali Forootani Peter Benner 57 1 0 14 May 2024
An invariance constrained deep learning network for PDE discovery Chao Chen Hui Li Xiaowei Jin PINN 32 1 0 06 Feb 2024
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels Da Long Wei W. Xing Aditi S. Krishnapriyan R. Kirby Shandian Zhe Michael W. Mahoney 55 0 0 09 Oct 2023
Deep Learning in Deterministic Computational Mechanics L. Herrmann Stefan Kollmannsberger AI4CE PINN 114 0 0 27 Sep 2023
Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data R. Stephany Christopher Earls 59 4 0 09 Sep 2023
Addressing Discontinuous Root-Finding for Subsequent Differentiability in Machine Learning, Inverse Problems, and Control Dan Johnson Ronald Fedkiw AI4CE 51 3 0 21 Jun 2023
DynaBench: A benchmark dataset for learning dynamical systems from low-resolution data Andrzej Dulny Andreas Hotho Anna Krause AI4CE 54 7 0 09 Jun 2023
Learning in latent spaces improves the predictive accuracy of deep neural operators Katiana Kontolati S. Goswami George Karniadakis Michael D. Shields AI4CE 88 22 0 15 Apr 2023
Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flows Owen Dugan Peter Y. Lu Rumen Dangovski Di Luo M. Soljavcić AI4CE 50 4 0 23 Feb 2023
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks S. Dong Yiran Wang 61 21 0 09 Oct 2022
Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition Yanqi Wu H. Aghamiry S. Operto Jianwei Ma 37 1 0 16 Aug 2022
Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion Hao Xu Junsheng Zeng Dongxiao Zhang DiffM 61 20 0 05 Aug 2022
Noise-aware Physics-informed Machine Learning for Robust PDE Discovery Pongpisit Thanasutives Takeshi Morita M. Numao Ken-ichi Fukui PINN AI4CE 110 19 0 26 Jun 2022
A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic Barbara Z Cunha C. Droz A. Zine Stéphane Foulard M. Ichchou AI4CE 61 91 0 13 Apr 2022
Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models Federico Fatone S. Fresca Andrea Manzoni AI4TS 62 16 0 25 Jan 2022
Multigoal-oriented dual-weighted-residual error estimation using deep neural networks Ayan Chakraborty T. Wick X. Zhuang Timon Rabczuk 48 8 0 21 Dec 2021
Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning Xiaoqian Chen Balasubramanya T. Nadiga Ilya Timofeyev 30 7 0 16 Dec 2021
Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks Jihun Han Yoonsang Lee AI4CE 63 10 0 02 Dec 2021
NeuralPDE: Modelling Dynamical Systems from Data Andrzej Dulny Andreas Hotho Anna Krause AI4CE 57 11 0 15 Nov 2021
A Neural Network Ensemble Approach to System Identification Elisa Negrini G. Citti L. Capogna 38 2 0 15 Oct 2021
Paradigm Shift Through the Integration of Physical Methodology and Data Science T. Miyamoto AI4CE 38 0 0 30 Sep 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 45 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 57 3 0 11 Aug 2021
Physics-constrained Deep Learning for Robust Inverse ECG Modeling Jianxin Xie B. Yao 82 22 0 26 Jul 2021
Discovering Sparse Interpretable Dynamics from Partial Observations Peter Y. Lu Joan Ariño Bernad Marin Soljacic AI4CE 83 25 0 22 Jul 2021
Physics-informed generative neural network: an application to troposphere temperature prediction Zhihao Chen Jie Gao Weikai Wang Zheng Yan AI4CE 67 18 0 08 Jul 2021
Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations Zhiming Zhang Yongming Liu 41 11 0 08 Jul 2021
Fully differentiable model discovery G. Both R. Kusters PINN 60 2 0 09 Jun 2021
Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data Junsheng Zeng Hao Xu Yuntian Chen Dongxiao Zhang 36 3 0 31 May 2021
Robust discovery of partial differential equations in complex situations Hao Xu Dongxiao Zhang AI4CE 79 29 0 31 May 2021
Physics-informed Spline Learning for Nonlinear Dynamics Discovery Fangzheng Sun Yang Liu Hao Sun AI4CE 55 28 0 05 May 2021
Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networks Jian Cheng Wong C. Ooi P. Chiu M. Dao PINN AI4CE 79 4 0 05 May 2021
Model discovery in the sparse sampling regime G. Both Georges Tod R. Kusters 59 3 0 02 May 2021
Multi-objective discovery of PDE systems using evolutionary approach M. Maslyaev A. Hvatov 105 5 0 11 Mar 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 60 439 0 04 Feb 2021
Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification L. Scarabosio 77 9 0 18 Jan 2021
Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data Hao Xu Dongxiao Zhang Nanzhe Wang 82 34 0 24 Nov 2020
Sparsely constrained neural networks for model discovery of PDEs G. Both Gijs Vermarien R. Kusters 18 5 0 09 Nov 2020
Data-driven Identification of 2D Partial Differential Equations using extracted physical features Kazem Meidani A. Farimani 54 17 0 20 Oct 2020
Discovery of Governing Equations with Recursive Deep Neural Networks Jia Zhao Jarrod Mau PINN 70 6 0 24 Sep 2020
System Identification Through Lipschitz Regularized Deep Neural Networks Elisa Negrini G. Citti L. Capogna 43 12 0 07 Sep 2020
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks Colby Wight Jia Zhao 82 225 0 09 Jul 2020
Physics informed deep learning for computational elastodynamics without labeled data Chengping Rao Hao Sun Yang Liu PINN AI4CE 86 226 0 10 Jun 2020
Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting Shitao Zheng T. Miyamoto K. Iwanami S. Shimizu Ryohei Kato 65 3 0 03 Jun 2020
DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization Rishikesh Ranade C. Hill Jay Pathak AI4CE 144 126 0 17 May 2020
Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Data Hao Xu Dongxiao Zhang Junsheng Zeng 70 57 0 16 May 2020
Physics-informed learning of governing equations from scarce data Zhao Chen Yang Liu Hao Sun PINN AI4CE 111 398 0 05 May 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 92 83 0 25 Apr 2020