Promising directions of machine learning for partial differential equations
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
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 …
Physics-informed neural operator for learning partial differential equations
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 …
data and physics constraints to learn the solution operator of a given family of parametric …
Enhancing computational fluid dynamics with machine learning
Abstract Machine learning is rapidly becoming a core technology for scientific computing,
with numerous opportunities to advance the field of computational fluid dynamics. Here we …
with numerous opportunities to advance the field of computational fluid dynamics. Here we …
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 …
On neural differential equations
P Kidger - ar**s
between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural …
between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural …
U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow
Numerical simulation of multiphase flow in porous media is essential for many geoscience
applications. Machine learning models trained with numerical simulation data can provide a …
applications. Machine learning models trained with numerical simulation data can provide a …
Modern Koopman theory for dynamical systems
The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …
algorithms emerging from modern computing and data science. First-principles derivations …