Data-Driven Deep Learning of Partial Differential Equations in Modal Space

15 October 2019

Papers citing "Data-Driven Deep Learning of Partial Differential Equations in Modal Space"

50 / 53 papers shown

Title
DUE: A Deep Learning Framework and Library for Modeling Unknown Equations Junfeng Chen Kailiang Wu D. Xiu 29 0 0 14 Apr 2025
Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ? Zijian Zhou Zhenya Yan 108 10 0 09 Dec 2024
Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems Yuán Chen Dongbin Xiu 34 0 0 27 Aug 2024
Operator Learning Using Random Features: A Tool for Scientific Computing Nicholas H. Nelsen Andrew M. Stuart 45 12 0 12 Aug 2024
Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models Kaiyuan Tan Peilun Li Thomas Beckers AI4CE 26 3 0 17 Jun 2024
Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning Junfeng Chen Kailiang Wu 42 3 0 15 May 2024
High Energy Density Radiative Transfer in the Diffusion Regime with Fourier Neural Operators Joseph Farmer Ethan Smith William Bennett Ryan McClarren 19 1 0 07 May 2024
Adaptive deep density approximation for stochastic dynamical systems Junjie He Qifeng Liao Xiaoliang Wan 27 2 0 05 May 2024
tLaSDI: Thermodynamics-informed latent space dynamics identification Jun Sur Richard Park Siu Wun Cheung Youngsoo Choi Yeonjong Shin AI4CE 32 4 0 09 Mar 2024
Dynamic Gaussian Graph Operator: Learning parametric partial differential equations in arbitrary discrete mechanics problems Chu Wang Jinhong Wu Yanzhi Wang Zhijian Zha Qi Zhou AI4CE 30 0 0 05 Mar 2024
Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications M. Haywood-Alexander Wei Liu Kiran Bacsa Zhilu Lai Eleni Chatzi AI4CE 22 9 0 31 Oct 2023
Fourier neural operator for real-time simulation of 3D dynamic urban microclimate W. Peng Shaoxiang Qin Senwen Yang Jianchun Wang Xue Liu Lei Wang AI4CE 23 30 0 08 Aug 2023
Learning Nonautonomous Systems via Dynamic Mode Decomposition Hannah Lu D. Tartakovsky AI4CE 14 1 0 27 Jun 2023
Energy-Dissipative Evolutionary Deep Operator Neural Networks Jiahao Zhang Shiheng Zhang Jie Shen Guang Lin 21 10 0 09 Jun 2023
Learning Stochastic Dynamical System via Flow Map Operator Yuán Chen D. Xiu AI4CE 27 15 0 05 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 37 5 0 26 Apr 2023
Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems Ce Zhang Kailiang Wu Zhihai He 35 0 0 15 Apr 2023
Physics informed WNO N. N. Tapas Tripura S. Chakraborty 33 28 0 12 Feb 2023
Discovering interpretable Lagrangian of dynamical systems from data Tapas Tripura S. Chakraborty 27 4 0 09 Feb 2023
Deep-OSG: Deep Learning of Operators in Semigroup Junfeng Chen Kailiang Wu AI4TS 23 6 0 07 Feb 2023
WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming Mengyi Tang Wenjing Liao R. Kuske S. Kang 17 16 0 06 Nov 2022
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks S. Dong Yiran Wang 29 20 0 09 Oct 2022
A variational neural network approach for glacier modelling with nonlinear rheology Tiangang Cui Zhongjian Wang Zhiwen Zhang 32 4 0 05 Sep 2022
Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue G. Tong Daniele E. Schiavazzi 35 3 0 05 Jul 2022
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence V. Churchill D. Xiu AI4CE 24 2 0 03 Jun 2022
Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data Seungjoon Lee Y. M. Psarellis Constantinos Siettos Ioannis G. Kevrekidis AI4CE 21 27 0 26 May 2022
Deep Learning of Chaotic Systems from Partially-Observed Data V. Churchill D. Xiu 40 12 0 12 May 2022
Wavelet neural operator: a neural operator for parametric partial differential equations Tapas Tripura S. Chakraborty 25 63 0 04 May 2022
Online Weak-form Sparse Identification of Partial Differential Equations Daniel Messenger E. Dall’Anese David M. Bortz 43 13 0 08 Mar 2022
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning V. Churchill Steve Manns Zhen Chen D. Xiu AI4CE 29 9 0 07 Mar 2022
Modeling unknown dynamical systems with hidden parameters Xiaohan Fu Weize Mao L. Chang D. Xiu 24 5 0 03 Feb 2022
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method Zhongjian Wang Jack Xin Zhiwen Zhang 39 15 0 02 Nov 2021
Neural Operator: Learning Maps Between Function Spaces Nikola B. Kovachki Zong-Yi Li Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 52 441 0 19 Aug 2021
Cell-average based neural network method for hyperbolic and parabolic partial differential equations Changxin Qiu Jue Yan 16 10 0 02 Jul 2021
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space Zhen Chen V. Churchill Kailiang Wu D. Xiu AI4CE 14 47 0 07 Jun 2021
Robust discovery of partial differential equations in complex situations Hao Xu Dongxiao Zhang AI4CE 25 28 0 31 May 2021
Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains Hengjie Wang R. Planas Aparna Chandramowlishwaran Ramin Bostanabad AI4CE 50 61 0 22 Apr 2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation Q. Du Yiqi Gu Haizhao Yang Chao Zhou 26 20 0 21 Mar 2021
A physics-informed operator regression framework for extracting data-driven continuum models Ravi G. Patel N. Trask M. Wood E. Cyr AI4CE 13 103 0 25 Sep 2020
An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient Haiyang He Jay Pathak 22 24 0 19 Jul 2020
Weak SINDy For Partial Differential Equations Daniel Messenger David M. Bortz 23 169 0 06 Jul 2020
GINNs: Graph-Informed Neural Networks for Multiscale Physics E. Hall S. Taverniers Markos A. Katsoulakis D. Tartakovsky PINN AI4CE 12 30 0 26 Jun 2020
Deep learning of free boundary and Stefan problems Sizhuang He P. Perdikaris 27 80 0 04 Jun 2020
Data-driven learning of non-autonomous systems Tong Qin Zhen Chen J. Jakeman D. Xiu 8 19 0 02 Jun 2020
The Random Feature Model for Input-Output Maps between Banach Spaces Nicholas H. Nelsen Andrew M. Stuart 21 141 0 20 May 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
Learning reduced systems via deep neural networks with memory Xiaohang Fu L. Chang D. Xiu 11 32 0 20 Mar 2020
Methods to Recover Unknown Processes in Partial Differential Equations Using Data Zhen Chen Kailiang Wu D. Xiu 22 3 0 05 Mar 2020
Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty Nicholas Galioto Alex Gorodetsky 17 32 0 04 Mar 2020
Data-Driven Discovery of Coarse-Grained Equations Joseph Bakarji D. Tartakovsky 37 32 0 30 Jan 2020