Operator learning using random features: A tool for scientific computing
Supervised operator learning centers on the use of training data, in the form of input-output
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
A practical existence theorem for reduced order models based on convolutional autoencoders
NR Franco, S Brugiapaglia - arXiv preprint arXiv:2402.00435, 2024 - arxiv.org
In recent years, deep learning has gained increasing popularity in the fields of Partial
Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain …
Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain …
Deep learning based reduced order modeling of Darcy flow systems with local mass conservation
We propose a new reduced order modeling strategy for tackling parametrized Partial
Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in …
Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in …
[图书][B] Statistical Foundations of Operator Learning
NH Nelsen - 2024 - search.proquest.com
This thesis studies operator learning from a statistical perspective. Operator learning uses
observed data to estimate mappings between infinite-dimensional spaces. It does so at the …
observed data to estimate mappings between infinite-dimensional spaces. It does so at the …