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 orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition
(DOD), for dimensionality reduction and reduced order modeling of parameter dependent …
(DOD), for dimensionality reduction and reduced order modeling of parameter dependent …
[HTML][HTML] Deep Learning-Based Rapid Flow Field Reconstruction Model with Limited Monitoring Point Information
P Wang, G Hu, W Hu, X Xue, J Tao, H Wen - Aerospace, 2024 - mdpi.com
The rapid reconstruction of the internal flow field within pressure vessel equipment based on
features from limited detection points was of significant value for online monitoring and the …
features from limited detection points was of significant value for online monitoring and the …
Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum
We consider a mixed formulation of parametrized elasticity problems in terms of stress,
displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce …
displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce …
Solvers for mixed finite element problems using Poincar\'e operators based on spanning trees
WM Boon - arXiv preprint arXiv:2410.08830, 2024 - arxiv.org
We propose an explicit construction of Poincar\'e operators for the lowest order finite
element spaces, by employing spanning trees in the grid. In turn, a stable decomposition of …
element spaces, by employing spanning trees in the grid. In turn, a stable decomposition of …