Gianluigi Rozza

SISSA, Mathematics Area, Faculty Member

Followers

Following

Co-authors

Mentions

Public Views

Full Professor in Numerical Analysis and Scientific Computing, PI of the ERC project AROMA-CFD

less

uploads

Papers

Pressure Data-Driven Variational Multiscale Reduced Order Models

SSRN Electronic Journal

Download

Efficient geometrical parametrization for finite‐volume‐based reduced order methods

International Journal for Numerical Methods in Engineering, 2020

SummaryIn this work, we present an approach for the efficient treatment of parametrized geometrie... more SummaryIn this work, we present an approach for the efficient treatment of parametrized geometries in the context of proper orthogonal decomposition (POD)‐Galerkin reduced order methods based on finite‐volume full order approximations. On the contrary to what is normally done in the framework of finite‐element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the discrete empirical interpolation method to handle together nonaffinity of the parametrization and nonlinearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a radial basis function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the nonorthogonal correction. In the second numerical example, the methodology is tested on a geometrically parametrized incompres...

Download

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

SpringerBriefs in mathematics, 2016

Download

A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation

Advances in Computational Mathematics

This work introduces a novel approach for data-driven model reduction of time-dependent parametri... more This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.

Download

Non-linear Manifold Reduced-Order Models with Convolutional Autoencoders and Reduced Over-Collocation Method

Journal of Scientific Computing

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model o... more Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear subspace approximations. Among the possible solutions, there are purely data-driven methods that leverage autoencoders and their variants to learn a latent representation of the dynamical system, and then evolve it in time with another architecture. Despite their success in many applications where standard linear techniques fail, more has to be done to increase the interpretability of the results, especially outside the training range and not in regimes characterized by an abundance of data. Not to mention that none of the knowledge on the physics of the model is exploited during the predictive phase. In order to overcome these weaknesses, we implement the non-linear manifold method introduced by Lee and Carlberg (J Comput Phys 404:108973, 2020) with...

Download

Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems

Journal of Scientific Computing

In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interact... more In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin–Temam projection scheme is applied to the incompressible Navier–Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid. The coupled problem is based on an Arbitrary Lagrangian Eulerian formulation, and the Proper Orthogonal Decomposition procedure is used for the generation of the reduced basis. We extend existing works on a segregated Reduced Order Model for Fluid-Structure Interaction to unsteady problems that couple an incompressible, Newtonian fluid with a linear elastic solid, in two spatial dimensions. We consider three test cases to assess the overall capabilities of the method: an unsteady, non-parametrized problem, a problem that presents a geometrical parametrization of the solid domain, and ...

Download

A Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks

2022 IEEE International Conference on Image Processing (ICIP)

Download

Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier–Stokes Equations

Vietnam Journal of Mathematics

This work investigates the use of sparse polynomial interpolation as a model order reduction meth... more This work investigates the use of sparse polynomial interpolation as a model order reduction method for the parametrized incompressible Navier–Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial approximations and comparing with established reduced basis techniques. Two numerical models serve to assess the accuracy of the reduced order models (ROMs), in particular parametric nonlinearities arising from curved geometries are investigated in detail. Besides the accuracy of the ROMs, other important features of the method are covered, such as offline-online splitting, run time and ease of implementation. The findings provide a clear indication that sparse polynomial interpolation is a valid instrument in the toolbox of ROM methods.

Download

Model Order Reduction for Boundary Condition Estimation in Casting Machinery

In continuous casting machinery, the molten metal solidifies in a mold. In order to control the c... more In continuous casting machinery, the molten metal solidifies in a mold. In order to control the casting process, a proper knowledge of the heat flux between the mold and the metal is crucial. This boundary condition can be estimated using thermocouples measurements inside the mold and solving an inverse problem. In this paper, we describe the application of model order reduction techniques to this problem that allow its solution in real time.

Download

A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation

SIAM Journal on Scientific Computing, 2020

Download

Model Reduction of Steady Fluid-Structure Interaction Problems with Free-Foem Deformations and Reduced Basis Methods

Preface to the first volume of Model Order Reduction

System- and Data-Driven Methods and Algorithms, 2021

Download

Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation

International Journal of Computational Fluid Dynamics, 2018

Download

Data-Driven Reduced Order Modelling for Patient-Specific Hemodynamics of Coronary Artery Bypass Grafts with Physical and Geometrical Parameters

Journal of Scientific Computing

Download

Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation

Cornell University - arXiv, Oct 26, 2022

Download

Hybrid Data-Driven Closure Strategies for Reduced Order Modeling

Download

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Journal of Scientific Computing

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, li... more Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the P...

Download

Reduced basis methods for time-dependent problems

Acta Numerica

Numerical simulation of parametrized differential equations is of crucial importance in the study... more Numerical simulation of parametrized differential equations is of crucial importance in the study of real-world phenomena in applied science and engineering. Computational methods for real-time and many-query simulation of such problems often require prohibitively high computational costs to achieve sufficiently accurate numerical solutions. During the last few decades, model order reduction has proved successful in providing low-complexity high-fidelity surrogate models that allow rapid and accurate simulations under parameter variation, thus enabling the numerical simulation of increasingly complex problems. However, many challenges remain to secure the robustness and efficiency needed for the numerical simulation of nonlinear time-dependent problems. The purpose of this article is to survey the state of the art of reduced basis methods for time-dependent problems and draw together recent advances in three main directions. First, we discuss structure-preserving reduced order model...

Download

MATHICSE Technical Report : Reduced order methods for uncertainty quantification problems

Download

POD-Galerkin reduced order model of the Boussinesq approximation for buoyancy-driven enclosed flows

A parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full O... more A parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full Order Model (FOM) is based on the finite volume approximation and the Boussinesq approximation is used for modeling the buoyancy. Therefore, there exists a two-way coupling between the incompressible Boussinesq equations and the energy equation. The reduced basis is constructed with a Proper Orthogonal Decomposition (POD) approach and to obtain the Reduced Order Model, a Galerkin projection of the governing equations onto the reduced basis is performed. The ROM is tested on a 2D differentially heated cavity of which the side wall temperatures are parametrized. The parametrization is done using a control function method. The aim of the method is to obtain homogeneous POD basis functions. The control functions are obtained solving a Laplacian function for temperature. Only one full order solution was required for the reduced basis creation. The obtained ROM is stable for different parameter...

Download