[HTML][HTML] A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
The present work proposes a framework for nonlinear model order reduction based on a
Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) …
Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) …
Transformers as neural operators for solutions of differential equations with finite regularity
Neural operator learning models have emerged as very effective surrogates in data-driven
methods for partial differential equations (PDEs) across different applications from …
methods for partial differential equations (PDEs) across different applications from …
[HTML][HTML] Nonlinear model order reduction for problems with microstructure using mesh informed neural networks
Many applications in computational physics involve approximating problems with
microstructure, characterized by multiple spatial scales in their data. However, these …
microstructure, characterized by multiple spatial scales in their data. However, these …
Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks
Mesh-based simulations play a key role when modeling complex physical systems that, in
many disciplines across science and engineering, require the solution to parametrized time …
many disciplines across science and engineering, require the solution to parametrized time …
Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating …
Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential
equations (PDEs), which provide a unified framework for describing various elliptic …
equations (PDEs), which provide a unified framework for describing various elliptic …
[HTML][HTML] Fast prediction and control of air core in hydrocyclone by machine learning to stabilize operations
Operation stability significantly impacts hydrocyclone separation performance during
wastewater treatment, sludge processing, and microplastic removal from water. The air core …
wastewater treatment, sludge processing, and microplastic removal from water. The air core …
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 …
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields
Deep Learning is having a remarkable impact on the design of Reduced Order Models
(ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for …
(ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for …
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task
that requires a significant number of model evaluations. The objective of this work is to …
that requires a significant number of model evaluations. The objective of this work is to …
Structure-Preserving Operator Learning
N Bouziani, N Boullé - arXiv preprint arXiv:2410.01065, 2024 - arxiv.org
Learning complex dynamics driven by partial differential equations directly from data holds
great promise for fast and accurate simulations of complex physical systems. In most cases …
great promise for fast and accurate simulations of complex physical systems. In most cases …