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 …

Physics-informed machine learning

GE Karniadakis, IG Kevrekidis, L Lu… - Nature Reviews …, 2021‏ - nature.com
Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

AF Psaros, X Meng, Z Zou, L Guo… - Journal of Computational …, 2023‏ - Elsevier
Neural networks (NNs) are currently changing the computational paradigm on how to
combine data with mathematical laws in physics and engineering in a profound way …

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 …

Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems

T Tripura, S Chakraborty - Computer Methods in Applied Mechanics and …, 2023‏ - Elsevier
With massive advancements in sensor technologies and Internet-of-things (IoT), we now
have access to terabytes of historical data; however, there is a lack of clarity on how to best …

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 …

A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations

R Mattey, S Ghosh - Computer Methods in Applied Mechanics and …, 2022‏ - Elsevier
A physics informed neural network (PINN) incorporates the physics of a system by satisfying
its boundary value problem through a neural network's loss function. The PINN approach …

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) …

[PDF][PDF] Integrating physics-based modeling with machine learning: A survey

J Willard, X Jia, S Xu, M Steinbach… - arxiv preprint arxiv …, 2020‏ - beiyulincs.github.io
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Integrating scientific knowledge with machine learning for engineering and environmental systems

J Willard, X Jia, S Xu, M Steinbach, V Kumar - ACM Computing Surveys, 2022‏ - dl.acm.org
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …