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Found 22 papers, 4 papers with code
SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study
In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems.
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 tackling complex problems for which classical methods might fail.
Multi-fidelity reduced-order surrogate modeling
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given system.
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.
A digital twin framework for civil engineering structures
This work proposes a predictive digital twin approach to the health monitoring, maintenance, and management planning of civil engineering structures.
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.
Multi-fidelity surrogate modeling using long short-term memory networks
Especially for parametrized, time dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data.
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.
Online structural health monitoring by model order reduction and deep learning algorithms
Within a structural health monitoring (SHM) framework, we propose a simulation-based classification strategy to move towards online damage localization.
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations
Our work is based on the use of deep autoencoders, which we employ for encoding and decoding a high fidelity approximation of the solution manifold.
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
In this work, we present the use of artificial neural networks applied to multi-fidelity regression problems.
Learning High-Order Interactions via Targeted Pattern Search
The algorithm relies on an interaction learning step based on a well-known frequent item set mining algorithm, and a novel dissimilarity-based interaction selection step that allows the user to specify the number of interactions to be included in the LR model.
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).
SUIHTER: A new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy
The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century.
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.
Fully convolutional networks for structural health monitoring through multivariate time series classification
We propose a novel approach to Structural Health Monitoring (SHM), aiming at the automatic identification of damage-sensitive features from data acquired through pervasive sensor systems.
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.
Statistical closure modeling for reduced-order models of stationary systems by the ROMES method
Rather than target these two types of errors, this work proposes to construct a statistical model for the state error itself; it achieves this by constructing statistical models for the generalized coordinates characterizing both the in-plane error (i. e., the error in the trial subspace) and a low-dimensional approximation of the out-of-plane error.
Numerical Analysis
