Scientific discovery in the age of artificial intelligence
Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment
and accelerate research, helping scientists to generate hypotheses, design experiments …
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
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 …
model equations, like Partial Differential Equations (PDE), as a component of the neural …
ClimaX: A foundation model for weather and climate
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 …
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
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 …
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
Physics-informed machine learning
Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …
Neural operator: Learning maps between function spaces with applications to pdes
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 …
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
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 …
modeling of complex dynamic processes across all corners of science and engineering …
Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
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 …
combine data with mathematical laws in physics and engineering in a profound way …
Pde-refiner: Achieving accurate long rollouts with neural pde solvers
Time-dependent partial differential equations (PDEs) are ubiquitous in science and
engineering. Recently, mostly due to the high computational cost of traditional solution …
engineering. Recently, mostly due to the high computational cost of traditional solution …
Laplace neural operator for solving differential equations
Neural operators map multiple functions to different functions, possibly in different spaces,
unlike standard neural networks. Hence, neural operators allow the solution of parametric …
unlike standard neural networks. Hence, neural operators allow the solution of parametric …