PINNpapers

Contributed by IDRL lab.

• PINNpapers
  • Introduction
  • Software
  • Papers on PINN Models
  • Papers on Parallel PINN
  • Papers on PINN Accerleration
  • Papers on Model Transfer & Meta-Learning
  • Papers on Probabilistic PINNs and Uncertainty Quantification
  • Papers on Applications
  • Papers on PINN Analysis

Introduction

Physics-Informed Neural Network (PINN) has achieved great success in scientific computing since 2017. In this repo, we list some representative work on PINNs. Feel free to distribute or use it!

Corrections and suggestions are welcomed.

A script for converting bibtex to the markdown used in this repo is also provided for your convenience.

Software

1. DeepXDE: A Deep Learning Library for Solving Differential Equations, Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis, SIAM Review, 2021. [paper][code]
2. NVIDIA SimNet™: An AI-Accelerated Multi-Physics Simulation Framework, Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Zhiwei Fang, Max Rietmann, Wonmin Byeon, Sanjay Choudhry, ICCS, 2021. [paper]
3. SciANN: A Keras wrapper for scientific computations and physics-informed deep learning using artificial neural networks, Ehsan Haghighat, Ruben Juanes, arXiv preprint arXiv:2005.08803, 2020. [paper][code]
4. Elvet -- a neural network-based differential equation and variational problem solver, Jack Y. Araz, Juan Carlos Criado, Michael Spannowsky, arXiv:2103.14575 [hep-lat, physics:hep-ph, physics:hep-th, stat], 2021. [paper][code]
5. TensorDiffEq: Scalable Multi-GPU Forward and Inverse Solvers for Physics Informed Neural Networks, Levi D. McClenny, Mulugeta A. Haile, Ulisses M. Braga-Neto, arXiv:2103.16034 [physics], 2021. [paper][code]
6. PyDEns: a Python Framework for Solving Differential Equations with Neural Networks, Alex Koryagin, er, Roman Khudorozkov, Sergey Tsimfer, arXiv:1909.11544 [cs, stat], 2019. [paper]
7. NeuroDiffEq: A Python package for solving differential equations with neural networks, Feiyu Chen, David Sondak, Pavlos Protopapas, Marios Mattheakis, Shuheng Liu, Devansh Agarwal, Marco Di Giovanni, Journal of Open Source Software, 2020. [paper][code]
8. Universal Differential Equations for Scientific Machine Learning, Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, Alan Edelman, arXiv:2001.04385 [cs, math, q-bio, stat], 2020. [paper][code]
9. NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations, Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, N Vinchhi, , Kaushik Balakrishnan, Devesh Upadhyay, Chris Rackauckas, arXiv:2107.09443 [cs], 2021. [paper][code]
10. IDRLnet: A Physics-Informed Neural Network Library, Wei Peng, Jun Zhang, Weien Zhou, Xiaoyu Zhao, Wen Yao, Xiaoqian Chen, arXiv:2107.04320 [cs, math], 2021. [paper][code]
11. NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators, Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George Em Karniadakis, UNKNOWN_JOURNAL, 2022. [paper][code]

Papers on PINN Models

1. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, M. Raissi, P. Perdikaris, G. E. Karniadakis, Journal of Computational Physics, 2019. [paper]
2. The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems, E Weinan, Bing Yu, Communications in Mathematics and Statistics, 2018. [paper]
3. DGM: A deep learning algorithm for solving partial differential equations, Justin Sirignano, Konstantinos Spiliopoulos, Journal of Computational Physics, 2018. [paper]
4. SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs, Amuthan A. Ramabathiran, Ramach, Prabhu ran, Journal of Computational Physics, 2021. [paper][code]
5. Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative, Yinlin Ye, Yajing Li, Hongtao Fan, Xinyi Liu, Hongbing Zhang, arXiv:2108.07490 [cs, math], 2021. [paper]
6. NH-PINN: Neural homogenization based physics-informed neural network for multiscale problems, Wing Tat Leung, Guang Lin, Zecheng Zhang, arXiv:2108.12942 [cs, math], 2021. [paper]
7. Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning, Ziming Liu, Yunyue Chen, Yuanqi Du, Max Tegmark, arXiv:2109.13901 [physics], 2021. [paper]
8. Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method, Yuntian Chen, Dou Huang, Dongxiao Zhang, Junsheng Zeng, Nanzhe Wang, Haoran Zhang, Jinyue Yan, Journal of Computational Physics, 2021. [paper]
9. Learning in Sinusoidal Spaces with Physics-Informed Neural Networks, Jian Cheng Wong, Chinchun Ooi, Abhishek Gupta, Yew-Soon Ong, arXiv:2109.09338 [physics], 2021. [paper]
10. HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks, Filipe de Avila Belbute-Peres, Yi-fan Chen, Fei Sha, NIPS, 2021. [paper]
11. Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries, AliKashefi, TapanMukerji, Journal of Computational Physics, 2022. [paper]
12. Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems, HanGao, Matthew J.Zahr, Jian-XunWang, Computer Methods in Applied Mechanics and Engineering, 2022. [paper]
13. PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network, Longxiang Jiang, Liyuan Wang, Xinkun Chu, Yonghao Xiao and Hao Zhang, arXiv:2208.04319 [cs.NE], 2022. [paper]
14. ModalPINN : an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors, * Ga´etan Raynaud , S´ebastien Houde, Fr´ed´erick P Gosselin*, Journal of Computational Physics, 2022. [paper]
15. ∆-PINNs: physics-informed neural networks on complex geometries, Francisco Sahli Costabal, Simone Pezzuto, Paris Perdikaris, Arxiv, 2022. [paper]
16. Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks, Wei Peng, Wen Yao, Weien Zhou, Xiaoya Zhang, Weijie Yao, ArXiv, 2022. [paper][code]

Papers on Parallel PINN

1. Parallel Physics-Informed Neural Networks via Domain Decomposition, Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis, arXiv:2104.10013 [cs], 2021. [paper]
2. Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations, Ben Moseley, Andrew Markham, Tarje Nissen-Meyer, arXiv:2107.07871 [physics], 2021. [paper]
3. PPINN: Parareal physics-informed neural network for time-dependent PDEs, Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis, Computer Methods in Applied Mechanics and Engineering, 2020. [paper]
4. When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?, Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi, arXiv:2109.09444 [cs, math, stat], 2021. [paper]
5. Scaling physics-informed neural networks to large domains by using domain decomposition, Ben Moseley, Andrew Markham, Tarje Nissen-Meyer, NIPS, 2021. [[paper](https://openreview.net/fo