The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running
Gaussian processes and random fields have a long history, covering multiple approaches to
representing spatial and spatio-temporal dependence structures, such as covariance …
representing spatial and spatio-temporal dependence structures, such as covariance …
The Matérn model: A journey through statistics, numerical analysis and machine learning
The Matern Model: A Journey Through Statistics, Numerical Analysis and Machine Learning
Page 1 Statistical Science 2024, Vol. 39, No. 3, 469–492 https://doi.org/10.1214/24-STS923 © …
Page 1 Statistical Science 2024, Vol. 39, No. 3, 469–492 https://doi.org/10.1214/24-STS923 © …
Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization
This work highlights an approach for incorporating realistic uncertainties into scientific
computing workflows based on finite elements, focusing on prevalent applications in …
computing workflows based on finite elements, focusing on prevalent applications in …
Stochastic analysis of geometrically imperfect thin cylindrical shells using topology-aware uncertainty models
Buckling of thin-shell structures is one of the most canonical problems in mechanics. In
practice, the buckling load and its deviation from theoretical prediction is often handled …
practice, the buckling load and its deviation from theoretical prediction is often handled …
Finite element representations of Gaussian processes: Balancing numerical and statistical accuracy
D Sanz-Alonso, R Yang - SIAM/ASA Journal on Uncertainty Quantification, 2022 - SIAM
The stochastic partial differential equation approach to Gaussian processes (GPs)
represents Matérn GP priors in terms of finite element basis functions and Gaussian …
represents Matérn GP priors in terms of finite element basis functions and Gaussian …
Stochastic modeling and identification of material parameters on structures produced by additive manufacturing
A methodology enabling the representation, sampling, and identification of spatially-
dependent stochastic material parameters on complex structures produced by additive …
dependent stochastic material parameters on complex structures produced by additive …
Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries
We present a stochastic modeling framework to represent and simulate spatially-dependent
geometrical uncertainties on complex geometries. While the consideration of random …
geometrical uncertainties on complex geometries. While the consideration of random …
A data-centric approach to generative modelling for 3D-printed steel
TJ Dodwell, LR Fleming… - … of the Royal …, 2021 - royalsocietypublishing.org
The emergence of additive manufacture (AM) for metallic material enables components of
near arbitrary complexity to be produced. This has potential to disrupt traditional engineering …
near arbitrary complexity to be produced. This has potential to disrupt traditional engineering …
Spatially-dependent material uncertainties in anisotropic nonlinear elasticity: Stochastic modeling, identification, and propagation
P Chen, J Guilleminot - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
This paper develops a stochastic model for the spatially-dependent material parameters
parameterizing anisotropic strain energy density functions. The construction is cast within …
parameterizing anisotropic strain energy density functions. The construction is cast within …
Covariance–based rational approximations of fractional SPDEs for computationally efficient Bayesian inference
The stochastic partial differential equation (SPDE) approach is widely used for modeling
large spatial datasets. It is based on representing a Gaussian random field u on R d as the …
large spatial datasets. It is based on representing a Gaussian random field u on R d as the …