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 …

Neural operators for accelerating scientific simulations and design

K Azizzadenesheli, N Kovachki, Z Li… - Nature Reviews …, 2024 - nature.com
Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

C Wu, M Zhu, Q Tan, Y Kartha, L Lu - Computer Methods in Applied …, 2023 - Elsevier
Physics-informed neural networks (PINNs) have shown to be effective tools for solving both
forward and inverse problems of partial differential equations (PDEs). PINNs embed the …

Respecting causality is all you need for training physics-informed neural networks

S Wang, S Sankaran, P Perdikaris - ar** strategies for physics-informed neural networks (PINNs) and their temporal decompositions
M Penwarden, AD Jagtap, S Zhe… - Journal of …, 2023 - Elsevier
Physics-informed neural networks (PINNs) as a means of solving partial differential
equations (PDE) have garnered much attention in the Computational Science and …