Promising directions of machine learning for partial differential equations
SL Brunton, JN Kutz - Nature Computational Science, 2024 - nature.com
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 …
Neural operators for accelerating scientific simulations and design
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 …
physical experiments. Numerical simulations are an alternative approach but are usually …
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 …
Convolutional neural operators for robust and accurate learning of PDEs
Although very successfully used in conventional machine learning, convolution based
neural network architectures--believed to be inconsistent in function space--have been …
neural network architectures--believed to be inconsistent in function space--have been …
[PDF][PDF] Convolutional neural operators
Although very successfully used in machine learning, convolution based neural network
architectures–believed to be inconsistent in function space–have been largely ignored in the …
architectures–believed to be inconsistent in function space–have been largely ignored in the …
Solving high-dimensional pdes with latent spectral models
Deep models have achieved impressive progress in solving partial differential equations
(PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output …
(PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output …
Representation equivalent neural operators: a framework for alias-free operator learning
Recently, operator learning, or learning mappings between infinite-dimensional function
spaces, has garnered significant attention, notably in relation to learning partial differential …
spaces, has garnered significant attention, notably in relation to learning partial differential …
A mathematical guide to operator learning
N Boullé, A Townsend - arXiv preprint arXiv:2312.14688, 2023 - arxiv.org
Operator learning aims to discover properties of an underlying dynamical system or partial
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
3D elastic wave propagation with a factorized Fourier neural operator (F-FNO)
Numerical simulations are computationally demanding in three-dimensional (3D) settings
but they are often required to accurately represent physical phenomena. Neural operators …
but they are often required to accurately represent physical phenomena. Neural operators …
A critical review of physics-informed machine learning applications in subsurface energy systems
Abstract Machine learning has emerged as a powerful tool in various fields, including
computer vision, natural language processing, and speech recognition. It can unravel …
computer vision, natural language processing, and speech recognition. It can unravel …