Scientific discovery in the age of artificial intelligence

H Wang, T Fu, Y Du, W Gao, K Huang, Z Liu… - Nature, 2023 - nature.com
Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment
and accelerate research, helping scientists to generate hypotheses, design experiments …

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 …

ClimaX: A foundation model for weather and climate

T Nguyen, J Brandstetter, A Kapoor, JK Gupta… - arXiv preprint arXiv …, 2023 - arxiv.org
Most state-of-the-art approaches for weather and climate modeling are based on physics-
informed numerical models of the atmosphere. These approaches aim to model the non …

A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data

L Lu, X Meng, S Cai, Z Mao, S Goswami… - Computer Methods in …, 2022 - Elsevier
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …

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 …

Neural operator: Learning maps between function spaces with applications to pdes

N Kovachki, Z Li, B Liu, K Azizzadenesheli… - Journal of Machine …, 2023 - jmlr.org
The classical development of neural networks has primarily focused on learning mappings
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

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 …

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 …

Pde-refiner: Achieving accurate long rollouts with neural pde solvers

P Lippe, B Veeling, P Perdikaris… - Advances in …, 2023 - proceedings.neurips.cc
Time-dependent partial differential equations (PDEs) are ubiquitous in science and
engineering. Recently, mostly due to the high computational cost of traditional solution …

Laplace neural operator for solving differential equations

Q Cao, S Goswami, GE Karniadakis - Nature Machine Intelligence, 2024 - nature.com
Neural operators map multiple functions to different functions, possibly in different spaces,
unlike standard neural networks. Hence, neural operators allow the solution of parametric …