no code implementations • 14 May 2024 • Simone Brivio, Stefania Fresca, Andrea Manzoni
In this paper, we consider a major extension of POD-DL-ROMs by enforcing the fulfillment of the governing physical laws in the training process -- that is, by making them physics-informed -- to compensate for possible scarce and/or unavailable data and improve the overall reliability.
no code implementations • 1 Mar 2024 • Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, Mara Tanelli
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.
no code implementations • 18 Oct 2023 • Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino
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.
1 code implementation • 1 Sep 2023 • Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz
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.
no code implementations • 3 Aug 2023 • Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni
We also assess, from a numerical standpoint, the importance of using GNNs, rather than classical dense deep neural networks, for the proposed framework.
1 code implementation • 2 Aug 2023 • Matteo Torzoni, Marco Tezzele, Stefano Mariani, Andrea Manzoni, Karen E. Willcox
This work proposes a predictive digital twin approach to the health monitoring, maintenance, and management planning of civil engineering structures.
no code implementations • 13 Nov 2022 • Paolo Conti, Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi
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.
no code implementations • 5 Aug 2022 • Paolo Conti, Mengwu Guo, Andrea Manzoni, Jan S. Hesthaven
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.
no code implementations • 12 May 2022 • Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi
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.
no code implementations • 5 Feb 2022 • Ludovica Cicci, Stefania Fresca, Andrea Manzoni
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.
no code implementations • 25 Jan 2022 • Federico Fatone, Stefania Fresca, Andrea Manzoni
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.
no code implementations • NeurIPS Workshop DLDE 2021 • Stefania Fresca, Federico Fatone, Andrea Manzoni
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.
no code implementations • 10 Jun 2021 • Stefania Fresca, Andrea Manzoni
Reduced order models (ROMs) relying, e. g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times.
no code implementations • 26 Mar 2021 • Luca Rosafalco, Matteo Torzoni, Andrea Manzoni, Stefano Mariani, Alberto Corigliano
Within a structural health monitoring (SHM) framework, we propose a simulation-based classification strategy to move towards online damage localization.
no code implementations • 10 Mar 2021 • Nicola R. Franco, Andrea Manzoni, Paolo Zunino
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.
no code implementations • 26 Feb 2021 • Mengwu Guo, Andrea Manzoni, Maurice Amendt, Paolo Conti, Jan S. Hesthaven
In this work, we present the use of artificial neural networks applied to multi-fidelity regression problems.
no code implementations • 23 Feb 2021 • Michela C. Massi, Nicola R. Franco, Francesca Ieva, Andrea Manzoni, Anna Maria Paganoni, Paolo Zunino
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.
no code implementations • 28 Jan 2021 • Stefania Fresca, Andrea Manzoni
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).
no code implementations • 9 Jan 2021 • Nicola Parolini, Luca Dede', Paola F. Antonietti, Giovanni Ardenghi, Andrea Manzoni, Edie Miglio, Andrea Pugliese, Marco Verani, Alfio Quarteroni
The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century.
1 code implementation • 2 Jun 2020 • Stefania Fresca, Andrea Manzoni, Luca Dedè, Alfio Quarteroni
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.
no code implementations • 12 Feb 2020 • Luca Rosafalco, Andrea Manzoni, Stefano Mariani, Alberto Corigliano
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.
no code implementations • 12 Jan 2020 • Stefania Fresca, Luca Dede, Andrea Manzoni
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.
1 code implementation • 9 Jan 2019 • Stefano Pagani, Andrea Manzoni, Kevin Carlberg
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