Scientific machine learning through physics–informed neural networks: Where we are and what's next

S Cuomo, VS Di Cola, F Giampaolo, G Rozza… - Journal of Scientific …, 2022 - Springer
Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges

Y Xu, S Kohtz, J Boakye, P Gardoni, P Wang - Reliability Engineering & …, 2023 - Elsevier
The computerized simulations of physical and socio-economic systems have proliferated in
the past decade, at the same time, the capability to develop high-fidelity system predictive …

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

S Wang, H Wang, P Perdikaris - Science advances, 2021 - science.org
Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …

When and why PINNs fail to train: A neural tangent kernel perspective

S Wang, X Yu, P Perdikaris - Journal of Computational Physics, 2022 - Elsevier
Physics-informed neural networks (PINNs) have lately received great attention thanks to
their flexibility in tackling a wide range of forward and inverse problems involving partial …

Physics-informed neural operator for learning partial differential equations

Z Li, H Zheng, N Kovachki, D **, H Chen… - ACM/JMS Journal of …, 2024 - dl.acm.org
In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

Understanding and mitigating gradient flow pathologies in physics-informed neural networks

S Wang, Y Teng, P Perdikaris - SIAM Journal on Scientific Computing, 2021 - SIAM
The widespread use of neural networks across different scientific domains often involves
constraining them to satisfy certain symmetries, conservation laws, or other domain …

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

S Wang, H Wang, P Perdikaris - Computer Methods in Applied Mechanics …, 2021 - Elsevier
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in
integrating physical models with gappy and noisy observational data, but they still struggle …

Self-adaptive loss balanced physics-informed neural networks

Z **ang, W Peng, X Liu, W Yao - Neurocomputing, 2022 - Elsevier
Physics-informed neural networks (PINNs) have received significant attention as a
representative deep learning-based technique for solving partial differential equations …

Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks

Q Zhu, Z Liu, J Yan - Computational Mechanics, 2021 - Springer
The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great
potential in the breakthrough of metal additive manufacturing (AM) process modeling, which …

PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

H Gao, L Sun, JX Wang - Journal of Computational Physics, 2021 - Elsevier
Recently, the advent of deep learning has spurred interest in the development of physics-
informed neural networks (PINN) for efficiently solving partial differential equations (PDEs) …