[HTML][HTML] POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to
overcome common limitations shared by conventional reduced order models (ROMs)–built …
overcome common limitations shared by conventional reduced order models (ROMs)–built …
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …
Multi-fidelity surrogate modeling using long short-term memory networks
When evaluating quantities of interest that depend on the solutions to differential equations,
we inevitably face the trade-off between accuracy and efficiency. Especially for …
we inevitably face the trade-off between accuracy and efficiency. Especially for …
[BOOK][B] Mathematical modelling of the human cardiovascular system: data, numerical approximation, clinical applications
Mathematical and numerical modelling of the human cardiovascular system has attracted
remarkable research interest due to its intrinsic mathematical difficulty and the increasing …
remarkable research interest due to its intrinsic mathematical difficulty and the increasing …
[HTML][HTML] Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
Highly accurate simulations of complex phenomena governed by partial differential
equations (PDEs) typically require intrusive methods and entail expensive computational …
equations (PDEs) typically require intrusive methods and entail expensive computational …
Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function
In order to simulate the cardiac function for a patient‐specific geometry, the generation of the
computational mesh is crucially important. In practice, the input is typically a set of …
computational mesh is crucially important. In practice, the input is typically a set of …
POD-enhanced deep learning-based reduced order models for the real-time simulation of cardiac electrophysiology in the left atrium
The numerical simulation of multiple scenarios easily becomes computationally prohibitive
for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models …
for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models …
Deep learning-based reduced order models in cardiac electrophysiology
Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies
on the numerical approximation of coupled nonlinear dynamical systems. These systems …
on the numerical approximation of coupled nonlinear dynamical systems. These systems …
[HTML][HTML] Approximation bounds for convolutional neural networks in operator learning
Abstract Recently, deep Convolutional Neural Networks (CNNs) have proven to be
successful when employed in areas such as reduced order modeling of parametrized PDEs …
successful when employed in areas such as reduced order modeling of parametrized PDEs …
Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs
To speed-up the solution of parametrized differential problems, reduced order models
(ROMs) have been developed over the years, including projection-based ROMs such as the …
(ROMs) have been developed over the years, including projection-based ROMs such as the …