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 …
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 …
Advances in magnetics roadmap on spin-wave computing
Magnonics addresses the physical properties of spin waves and utilizes them for data
processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency …
processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency …
Solving and learning nonlinear PDEs with Gaussian processes
We introduce a simple, rigorous, and unified framework for solving nonlinear partial
differential equations (PDEs), and for solving inverse problems (IPs) involving the …
differential equations (PDEs), and for solving inverse problems (IPs) involving the …
Learning physics-based models from data: perspectives from inverse problems and model reduction
This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …
inverse problems and model reduction. These fields develop formulations that integrate data …
The random feature model for input-output maps between banach spaces
Well known to the machine learning community, the random feature model is a parametric
approximation to kernel interpolation or regression methods. It is typically used to …
approximation to kernel interpolation or regression methods. It is typically used to …
[图书][B] Parameter estimation and inverse problems
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at
New Mexico Tech and is designed to be accessible to typical graduate students in the …
New Mexico Tech and is designed to be accessible to typical graduate students in the …
A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion
We present a computational framework for estimating the uncertainty in the numerical
solution of linearized infinite-dimensional statistical inverse problems. We adopt the …
solution of linearized infinite-dimensional statistical inverse problems. We adopt the …
The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications
Mathematical and numerical modelling of the cardiovascular system is a research topic that
has attracted remarkable interest from the mathematical community because of its intrinsic …
has attracted remarkable interest from the mathematical community because of its intrinsic …
[图书][B] Numerical models for differential problems
A Quarteroni, S Quarteroni - 2009 - Springer
Alfio Quarteroni Third Edition Page 1 MS&A – Modeling, Simulation and Applications 16
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …