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 …
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 …
Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation
Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the
solution of problems in cardiac mechanics is crucial to allow the translation of patient …
solution of problems in cardiac mechanics is crucial to allow the translation of patient …
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 …
Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models
M Tomasetto, A Manzoni, F Braghin - arXiv preprint arXiv:2409.05709, 2024 - arxiv.org
Steering a system towards a desired target in a very short amount of time is challenging from
a computational standpoint. Indeed, the intrinsically iterative nature of optimal control …
a computational standpoint. Indeed, the intrinsically iterative nature of optimal control …
PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs
The coupling of Proper Orthogonal Decomposition (POD) and deep learning-based ROMs
(DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly …
(DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly …
On latent dynamics learning in nonlinear reduced order modeling
In this work, we present the novel mathematical framework of latent dynamics models
(LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our …
(LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our …
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 …
Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs
Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-
established class of accurate surrogate models for complex physical systems described by …
established class of accurate surrogate models for complex physical systems described by …