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Found 10 papers, 1 papers with code
Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks
We also assess, from a numerical standpoint, the importance of using GNNs, rather than classical dense deep neural networks, for the proposed framework.
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 costs, which might become prohibitive when approximating steady-state solutions of PDEs for multiple combinations of control parameters and initial conditions.
Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches
Micro-Electro-Mechanical-Systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications.
Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs
To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as surrogate models obtained via a machine learning approach.
Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e. g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear time-dependent parametrized PDEs.
Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e. g., through proper orthogonal decomposition (POD) - when applied to nonlinear time-dependent parametrized PDEs.
Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
Reduced order models (ROMs) relying, e. g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times.
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, e. g., through proper orthogonal decomposition (POD) - when applied to nonlinear time-dependent parametrized partial differential equations (PDEs).
Deep learning-based reduced order models in cardiac electrophysiology
These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables.
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e. g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs, because of the fundamental assumption of linear superimposition of modes they are based on.
