A tutorial on Bayesian inference to identify material parameters in solid mechanics
The aim of this contribution is to explain in a straightforward manner how Bayesian inference
can be used to identify material parameters of material models for solids. Bayesian …
can be used to identify material parameters of material models for solids. Bayesian …
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 …
[图书][B] Nonlinear Data Assimilation for high-dimensional systems: -with geophysical applications
PJ Van Leeuwen, Y Cheng, S Reich, PJ van Leeuwen - 2015 - Springer
In this chapter the state-of-the-art in data assimilation for high-dimensional highly nonlinear
systems is reviewed, and recent developments are highlighted. This knowledge is available …
systems is reviewed, and recent developments are highlighted. This knowledge is available …
[HTML][HTML] Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels
High-resolution (HR) information of fluid flows, although preferable, is usually less
accessible due to limited computational or experimental resources. In many cases, fluid data …
accessible due to limited computational or experimental resources. In many cases, fluid data …
[图书][B] Introduction to uncertainty quantification
TJ Sullivan - 2015 - books.google.com
This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …
quantification (UQ) are defined and an overview of the range of mathematical methods by …
Data assimilation
A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …
development of principled methodologies for the seamless integration of (often vast) data …
The Bayesian approach to inverse problems
M Dashti, AM Stuart - arXiv preprint arXiv:1302.6989, 2013 - arxiv.org
These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …
formulation of, and development of algorithms for, the Bayesian approach to inverse …
Inverse problems: a Bayesian perspective
AM Stuart - Acta numerica, 2010 - cambridge.org
The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …
importance, and has also generated substantial mathematical and computational …
MCMC methods for functions: modifying old algorithms to make them faster
Many problems arising in applications result in the need to probe a probability distribution
for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion …
for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion …
Ensemble Kalman methods for inverse problems
Abstract The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen
1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state …
1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state …