Research papers for Physics-Informed Neural Network (PINN)

This repository is inspired by Intelligent Design and Robus Learning Laboratory (IDRL).

This is structured to first help readers gain a general understanding of Physics-Informed Neural Network, with a targeted focus on fluid-mechanics-related papers later. Finally, links to different PINN packages, frameworks, and non-PINN papers are shown in the last section.

Last updated: 2024-10-07

Table of Content

• Original Paper
• Literature Reviews
• Fluid Mechanics
• PINN Packages
• Frameworks, Mitigating Pathologies
• Non-PINN Papers
• Acknowledgement

Original Paper

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][code]

Literature Reviews

1. Physics-informed machine learning, George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, Liu Yang, Nat. Rev. Phys., 2021. [paper]
2. Physics-informed neural networks (PINNs) for fluid mechanics: a review, Shengze Cai, Zhiping Mao, Zhicheng Wang, Yin, Minglang, George Em Karniadakis, Acta Mech. Sin., 2022. [paper]
3. Deep learning in computational mechanics, Stefan Kollmannsberger, Davide D'Angella, Moritz Jokeit, Leon Herrmann, UNKNOWN_JOURNAL, 2021. [paper]
4. Scientific Machine Learning Through Physics--Informed Neural Networks: Where we are and What's Next, Salvatore Cuomo, Vincenzo Schiano Di Cola, Giampaolo, Fabio, Gianluigi Rozza, Maziar Raissi, Piccialli, Francesco, J. Sci. Comput., 2022. [paper]
5. The old and the new: Can physics-informed deep-learning replace traditional linear solvers?, Stefano Markidis, Front. Big Data, 2021. [paper]
6. Physics-informed neural networks for heat transfer problems, Shengze Cai, Zhicheng Wang, Sifan Wang, Perdikaris, Paris, George Em Karniadakis, J. Heat Transfer, 2021. [paper]
7. Physics-informed neural network (PINN) evolution and beyond: A systematic literature review and bibliometric analysis, Zaharaddeen Karami Lawal, Hayati Yassin, Daphne Teck Ching Lai, Azam Che Idris, Big Data Cogn. Comput., 2022. [paper]
8. A review of physics-informed machine learning in fluid mechanics, Pushan Sharma, Wai Tong Chung, Bassem Akoush, Ihme, Matthias, Energies, 2023. [paper]
9. A review of physics-informed machine learning in fluid mechanics, Pushan Sharma, Wai Tong Chung, Bassem Akoush, Ihme, Matthias, Energies, 2023. [paper]

Fluid Mechanics

1. Physics-informed deep learning for incompressible laminar flows, Chengping Rao, Hao Sun, Yang Liu, Theor. Appl. Mech. Lett., 2020. [paper][code]
2. Investigation of physics-informed deep learning for the prediction of parametric, three-dimensional flow based on boundary data, Philip Heger, Daniel Hilger, Markus Full, Hosters, Norbert, Comput. Fluids, 2024. [paper]
3. On physics-informed deep learning for solving Navier-stokes equations, Cahya Amalinadhi, Pramudita S Palar, Rafael Stevenson, Lavi Zuhal, 2022. [paper]
4. NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations, Xiaowei Jin, Shengze Cai, Hui Li, Karniadakis, George Em, J. Comput. Phys., 2021. [paper]
5. Physics-informed neural networks for high-speed flows, Zhiping Mao, Ameya D Jagtap, George Em Karniadakis, Comput. Methods Appl. Mech. Eng., 2020. [paper]
6. Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations, Christopher J Arthurs, Andrew P King, J. Comput. Phys., 2021. [paper]
7. Dynamic weight strategy of physics-informed neural networks for the 2D Navier-Stokes equations, Shirong Li, Xinlong Feng, Entropy (Basel), 2022. [paper]
8. Physics-informed neural networks for solving Reynolds-averaged Navier--Stokes equations, Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, Ricardo Vinuesa, Phys. Fluids (1994), 2022. [paper][code]
9. Turbulence modeling for physics-informed neural networks: Comparison of different RANS models for the backward-facing step flow, Fabian Pioch, Jan Hauke Harmening, Andreas Maximilian Muller, Franz-Josef Peitzmann, Dieter Schramm, Ould el Moctar, Fluids, 2023. [paper]
10. Three-dimensional physics-informed neural network simulation in coronary artery trees, Nursultan Alzhanov, Eddie Y K Ng, Yong Zhao, Fluids, 2024. [paper]
11. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Luning Sun, Han Gao, Shaowu Pan, Jian-Xun Wang, Comput. Methods Appl. Mech. Eng., 2020. [paper]
12. On the choice of activation functions in physics-informed neural network for solving incompressible fluid flows, Duong V Dung, Nguyen D Song, Pramudita S Palar, Lavi R Zuhal, American Institute of Aeronautics and Astronautics, 2023. [paper]

PINN Packages

1. DeepXDE: A deep learning library for solving differential equations, Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis, SIAM Review, 2021. [paper][code][documentation]
2. SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks, Ehsan Haghighat, Ruben Juanes, Comput. Methods Appl. Mech. Eng., 2021. [paper][code][documentation]
3. NVIDIA SimNet™: An AI-Accelerated Multi-Physics Simulation Framework, Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Fang, Zhiwei, Max Rietmann, Wonmin Byeon, Sanjay Choudhry, ICCS, 2021. [paper]

Frameworks, and mitigating pathologies

1. Understanding and mitigating gradient pathologies in physics-informed neural networks, Sifan Wang, Yujun Teng, Paris Perdikaris, UNKNOWN_JOURNAL, 2020. [paper]
2. An extended physics informed neural network for preliminary analysis of parametric optimal control problems, Nicola Demo, Maria Strazzullo, Gianluigi Rozza, UNKNOWN_JOURNAL, 2021. [paper]
3. Physics-informed neural networks with hard constraints for inverse design, Lu Lu, Rapha{"e}l Pestourie, Wenjie Yao, Wang, Zhicheng, Francesc Verdugo, Steven G Johnson, SIAM J. Sci. Comput., 2021. [paper][code]
4. Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Ameya D Jagtap, Kenji Kawaguchi, George Em Karniadakis, Proc. Math. Phys. Eng. Sci., 2020. [paper]
5. A practical PINN framework for multi-scale problems with multi-magnitude loss terms, Yong Wang, Yanzhong Yao, Jiawei Guo, Zhiming Gao, J. Comput. Phys., 2024. [paper]

Non-PINN papers

1. Navier--stokes Generative Adversarial Network: a physics-informed deep learning model for fluid flow generation, Pin Wu, Kaikai Pan, Lulu Ji, Siquan Gong, Feng, Weibing, Wenyan Yuan, Christopher Pain, Neural Comput. Appl., 2022. [paper]
2. Geometry aware physics informed neural network surrogate for solving Navier--Stokes equation (GAPINN), Jan Oldenburg, Finja Borowski, Alper {"O}ner, Klaus-Peter Schmitz, Michael Stiehm, Adv. Model. Simul. Eng. Sci., 2022. [paper]
3. Physics-driven learning of the steady Navier-Stokes equations using deep Convolutional neural networks, Hao Ma, Yuxuan Zhang, Nils Thuerey, Xiangyu Hu, Oskar J Haidn, arXiv physics.flu-dyn 2106.09301, 2021. [paper]

Acknowledgements

This project uses code from PINNpapers by weipengOO98, available at https://github.com/idrl-lab/PINNpapers/tree/main under the MIT License.