Long-time integration of parametric evolution equations with physics-informed DeepONets

9 June 2021

Papers citing "Long-time integration of parametric evolution equations with physics-informed DeepONets"

29 / 29 papers shown

Title
TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation Dibyajyoti Nayak Somdatta Goswami 63 0 0 22 May 2025
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 79 157 0 24 Mar 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 102 710 0 19 Mar 2021
Evolutional Deep Neural Network Yifan Du T. Zaki 78 73 0 18 Mar 2021
Machine learning accelerated computational fluid dynamics Dmitrii Kochkov Jamie A. Smith Ayya Alieva Qing Wang M. Brenner Stephan Hoyer AI4CE 143 876 0 28 Jan 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 197 461 0 18 Dec 2020
$NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework$ NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework O. Hennigh S. Narasimhan M. A. Nabian Akshay Subramaniam Kaustubh Tangsali M. Rietmann J. Ferrandis Wonmin Byeon Z. Fang S. Choudhry PINN AI4CE 135 129 0 14 Dec 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 92 461 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 924 0 28 Jul 2020
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks Colby Wight Jia Zhao 80 225 0 09 Jul 2020
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains Matthew Tancik Pratul P. Srinivasan B. Mildenhall Sara Fridovich-Keil N. Raghavan Utkarsh Singhal R. Ramamoorthi Jonathan T. Barron Ren Ng 135 2,450 0 18 Jun 2020
Array Programming with NumPy Charles R. Harris K. Millman S. Walt R. Gommers Pauli Virtanen ... Tyler Reddy Warren Weckesser Hameer Abbasi C. Gohlke T. Oliphant 161 15,066 0 18 Jun 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 148 1,104 0 21 Feb 2020
Understanding and mitigating gradient pathologies in physics-informed neural networks Sizhuang He Yujun Teng P. Perdikaris AI4CE PINN 116 297 0 13 Jan 2020
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 87 246 0 27 Nov 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,162 0 08 Oct 2019
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs Xuhui Meng Zhen Li Dongkun Zhang George Karniadakis PINN AI4CE 84 456 0 23 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 234 1,389 0 27 Aug 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 101 1,549 0 10 Jul 2019
$Transfer learning enhanced physics informed neural network for phase-field modeling of fracture$ Transfer learning enhanced physics informed neural network for phase-field modeling of fracture S. Goswami C. Anitescu S. Chakraborty Timon Rabczuk PINN 88 614 0 04 Jul 2019
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks N. Geneva N. Zabaras AI4CE 71 275 0 13 Jun 2019
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks Georgios Kissas Yibo Yang E. Hwuang W. Witschey John A. Detre P. Perdikaris AI4CE 132 375 0 13 May 2019
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data Yinhao Zhu N. Zabaras P. Koutsourelakis P. Perdikaris PINN AI4CE 121 871 0 18 Jan 2019
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 167 1,456 0 22 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 128 1,393 0 30 Sep 2017
Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks Chelsea Finn Pieter Abbeel Sergey Levine OOD 841 11,961 0 09 Mar 2017
Inferring solutions of differential equations using noisy multi-fidelity data M. Raissi P. Perdikaris George Karniadakis AI4CE 67 290 0 16 Jul 2016
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 179 2,824 0 20 Feb 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 2.1K 150,433 0 22 Dec 2014