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Gianluigi Rozza

Publications and source records attributed to Gianluigi Rozza.

At least 109 records · Page 6Linked to original sources
arXiv2023

A multi-fidelity approach coupling parameter space reduction and non-intrusive POD with application to structural optimization of passenger ship hulls

Nowadays, the shipbuilding industry is facing a radical change towards solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation, and by reducing the metal raw materials used during the manufacturing. This work focuses on the last aspect by presenting a complete structural optimization pipeline for modern passenger ship hulls which exploits advanced model order reduction techniques to reduce the dimensionality of both input parameters and outputs of interest. We introduce a novel approach which incorporates parameter space reduction through active subspaces into the proper orthogonal decomposition with interpolation method. This is done in a multi-fidelity setting. We test the whole framework on a simplified model of a midship section and on the full model of a passenger ship, controlled by 20 and 16 parameters, respectively. We present a comprehensive error analysis and show the capabilities and usefulness of the methods especially during the preliminary design phase, finding new unconsidered designs while handling high dimensional parameterizations.

math.NA↗
arXiv2023

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

math.NA↗
arXiv2023

Deep Reinforcement Learning for the Heat Transfer Control of Pulsating Impinging Jets

This research study explores the applicability of Deep Reinforcement Learning (DRL) for thermal control based on Computational Fluid Dynamics. To accomplish that, the forced convection on a hot plate prone to a pulsating cooling jet with variable velocity has been investigated. We begin with evaluating the efficiency and viability of a vanilla Deep Q-Network (DQN) method for thermal control. Subsequently, a comprehensive comparison between different variants of DRL is conducted. Soft Double and Duel DQN achieved better thermal control performance among all the variants due to their efficient learning and action prioritization capabilities. Results demonstrate that the soft Double DQN outperforms the hard Double DQN. Moreover, soft Double and Duel can maintain the temperature in the desired threshold for more than 98% of the control cycle. These findings demonstrate the promising potential of DRL in effectively addressing thermal control systems.

math.NA↗
arXiv2023

A Reduced Order Model formulation for left atrium flow: an Atrial Fibrillation case

A data-driven Reduced Order Model (ROM) based on a Proper Orthogonal Decomposition - Radial Basis Function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of Atrial Fibrillation (AF). The Full Order Model (FOM) is represented by incompressible Navier-Stokes equations, discretized with a Finite Volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.

physics.flu-dyn↗
arXiv2023

Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions

Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the linearized Euler equations of gas dynamics, the equations of compressible linear elasticity and the Dirac-Klein-Gordon system. FS were studied to approximate PDEs of mixed elliptic and hyperbolic type in the same domain. For this and other reasons, the versatility of the discontinuous Galerkin method (DGM) represents the best approximation space for FS. We implement a distributed memory solver for stationary FS in deal.II. Our focus is model order reduction. Since FS model hyperbolic PDEs, they often suffer from a slow Kolmogorov n-width decay. We develop two approaches to tackle this problem. The first is domain decomposable reduced-order models (DD-ROMs). We will show that the DGM offers a natural formulation of DD-ROMs, in particular regarding interface penalties, compared to the continuous finite element method. We also develop new repartitioning strategies to obtain more efficient local approximations of the solution manifold. The second approach involves graph neural networks used to infer the limit of a succession of projection-based linear ROMs corresponding to lower viscosity constants: the heuristic behind is to develop a multi-fidelity super-resolution paradigm to mimic the mathematical convergence to vanishing viscosity solutions while exploiting to the most interpretable and certified projection-based ROMs.

math.NA↗
arXiv2023

Explicable hyper-reduced order models on nonlinearly approximated solution manifolds of compressible and incompressible Navier-Stokes equations

A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the reduced space needed to approximate with sufficient accuracy the solution manifold. To solve this problem, neural networks, in the form of different architectures, have been employed to build accurate nonlinear regressions of the solution manifolds. However, the majority of the implementations are non-intrusive black-box surrogate models, and only a part of them perform dimension reduction from the number of degrees of freedom of the discretized parametric models to a latent dimension. We present a new intrusive and explicable methodology for reduced-order modelling that employs neural networks for solution manifold approximation but that does not discard the physical and numerical models underneath in the predictive/online stage. We will focus on autoencoders used to compress further the dimensionality of linear approximants of solution manifolds, achieving in the end a nonlinear dimension reduction. After having obtained an accurate nonlinear approximant, we seek for the solutions on the latent manifold with the residual-based nonlinear least-squares Petrov-Galerkin method, opportunely hyper-reduced in order to be independent from the number of degrees of freedom. New adaptive hyper-reduction strategies are developed along with the employment of local nonlinear approximants. We test our methodology on two nonlinear time-dependent parametric benchmarks involving a supersonic flow past a NACA airfoil with changing Mach number and an incompressible turbulent flow around the Ahmed body with changing slant angle.

math.NA↗
arXiv2023

Generative Models for the Deformation of Industrial Shapes with Linear Geometric Constraints: model order and parameter space reductions

Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization studies require the realization of response surfaces from the parameters that determine the geometrical deformations to relevant outputs to be optimized. In this context, a crucial aspect to be addressed are the limited resources at disposal to computationally generate different geometries or to physically obtain them from direct measurements. This is the case for patient-specific biomedical applications for example. When additional linear geometrical constraints need to be imposed, the computational costs increase substantially. Such constraints include total volume conservation, barycenter location and fixed moments of inertia. We develop a new paradigm that employs generative models from machine learning to efficiently sample new geometries with linear constraints. A consequence of our approach is the reduction of the parameter space from the original geometrical parametrization to a low-dimensional latent space of the generative models. Crucial is the assessment of the quality of the distribution of the constrained geometries obtained with respect to physical and geometrical quantities of interest. Non-intrusive model order reduction is enhanced since smaller parametric spaces are considered. We test our methodology on two academic test cases: a mixed Poisson problem on the 3d Stanford bunny with fixed barycenter deformations and the multiphase turbulent incompressible Navier-Stokes equations for the Duisburg test case with fixed volume deformations of the naval hull.

math.NA↗
arXiv2023

An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain-decomposition (DD) methods and reduced-order modelling (ROM). In particular, we consider an optimisation-based domain-decomposition algorithm for the parameter-dependent stationary incompressible Navier-Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal-control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward-facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain-decomposition algorithm.

math.NA↗
arXiv2023

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.

math.NA↗
arXiv2023

A Comparison of Data-Driven Reduced Order Models for the Simulation of Mesoscale Atmospheric Flow

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order models that have successfully reduced the computational time for different applications in computational fluid dynamics while preserving accuracy: Dynamic Mode Decomposition (DMD), Hankel Dynamic Mode Decomposition (HDMD), and Proper Orthogonal Decomposition with Interpolation (PODI). The three methods are compared in terms of computational time and accuracy in the simulation of two well-known benchmarks for mesoscale flow. The accuracy of the DMD and HDMD solutions deteriorates rather quickly as the forecast time window expands, although these methods are designed to predict the dynamics of a system. The reason is likely the strong nonlinearity in the benchmark flows. The PODI solution is accurate for the entire duration of the time interval of interest thanks to the use of interpolation with radial basis functions. This holds true also when the model features a physical parameter expected to vary in a given range, as is typically the case in weather prediction.

physics.flu-dyn↗
arXiv2023

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low intrinsic dimensionality. By introducing a low dimensional bias we can fight the curse of dimensionality affecting these quantities of interest, especially for many-query applications. We seek a gradient-based reduction of the parameter space through linear active subspaces or a nonlinear transformation of the input space. Then we build a low-fidelity response surface based on such reduction, thus enabling nonlinear autoregressive multi-fidelity Gaussian process regression without the need of running new simulations with simplified physical models. This has a great potential in the data scarcity regime affecting many engineering applications. In this work we present a new multi-fidelity approach that involves active subspaces and the nonlinear level-set learning method, starting from the preliminary analysis previously conducted in Romor et al. 2020. The proposed framework is tested on two high-dimensional benchmark functions, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces.

math.NA↗
arXiv2023

An extended physics informed neural network for preliminary analysis of parametric optimal control problems

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally expensive most of all in a real-time and many-query setting. Thus, our main goal is to provide a physics informed learning paradigm to simulate parametrized phenomena in a small amount of time. The physics information will be exploited in many ways, in the loss function (standard physics informed neural networks), as an augmented input (extra feature employment) and as a guideline to build an effective structure for the neural network (physics informed architecture). These three aspects, combined together, will lead to a faster training phase and to a more accurate parametric prediction. The methodology has been tested for several equations and also in an optimal control framework.

cs.LG↗
arXiv2023

A unified steady and unsteady formulation for hydrodynamic potential flow simulations with fully nonlinear free surface boundary conditions

This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a mathematical formulation and a numerical treatment that can be used both to carry out transient simulations, and to compute steady solutions -- for any flow admitting them. In the literature on numerical towing tank in fact, steady and unsteady fully nonlinear potential flow solvers are characterized by different mathematical formulations. The kinematic and dynamic fully nonlinear free surface boundary conditions are discussed, and in particular it is proven that the kinematic free surface boundary condition, written in semi-Lagrangian form, can be manipulated to derive an alternative non penetration boundary condition by all means identical to the one used on the surface of floating bodies or on the basin bottom. The simplified mathematical problem obtained is discretized over space and time via Boundary Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme, respectively. The results confirm that the solver implemented is able to solve steady potential flow problems just by eliminating null time derivatives in the unsteady formulation. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.

math.NA↗
arXiv2023

Reduced order models for the buckling of hyperelastic beams

In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications on their design for structural analysis and health. When the beams are exposed to external forces, their equilibrium state can undergo to a sudden variation. This happens when a compression, acting along the axial boundaries, exceeds a certain critical value. Linear elasticity models are not complex enough to capture the so-called beam's buckling, and nonlinear constitutive relations, as the hyperelastic laws, are required to investigate this behavior, whose mathematical counterpart is represented by bifurcating phenomena. The numerical analysis of the bifurcating modes and the post-buckling behavior, is usually unaffordable by means of standard high-fidelity techniques such (as the Finite Element method) and the efficiency of Reduced Order Models (ROMs), e.g.\ based on Proper Orthogonal Decomposition (POD), are necessary to obtain consistent speed-up in the reconstruction of the bifurcation diagram. The aim of this work is to provide insights regarding the application of POD-based ROMs for buckling phenomena occurring for 2-D and 3-D beams governed by different constitutive relations. The benchmarks will involve multi-parametric settings with geometrically parametrized domains, where the buckling's location depends on the material and geometrical properties induced by the parameter. Finally, we exploit the acquired notions from these toy problems, to simulate a real case scenario coming from the Norwegian petroleum industry.

math.NA↗
arXiv2023

A physics-based reduced order model for urban air pollution prediction

This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in pollutant emissions due to urbanization and its adverse effects on human health. The proposed methodology involves solving the linear advection-diffusion problem, where the solution of the Reynolds-averaged Navier-Stokes equations gives the convective field. At the same time, the source term consists of an empirical time series. However, the computational requirements of this approach, including microscale spatial resolution, repeated evaluation, and low time scale, necessitate the use of high-performance computing facilities, which can be a bottleneck for real-time monitoring. To address this challenge, a problem-specific methodology was developed that leverages a data-driven approach based on Proper Orthogonal Decomposition with regression (POD-R) coupled with Galerkin projection (POD-G) endorsed with the discrete empirical interpolation method (DEIM). The proposed method employs a feedforward neural network to non-intrusively retrieve the reduced-order convective operator required for online evaluation. The numerical framework was validated on synthetic emissions and real wind measurements. The results demonstrate that the proposed approach significantly reduces the computational burden of the traditional approach and is suitable for real-time air quality monitoring. Overall, the study advances the field of reduced order modeling and highlights the potential of data-driven approaches in environmental modeling and large-scale simulations.

math.NA↗
arXiv2023

A Continuous Convolutional Trainable Filter for Modelling Unstructured Data

Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.

cs.LG↗
arXiv2023

Filter stabilization for the mildly compressible Euler equations with application to atmosphere dynamics simulations

We present a filter stabilization technique for the mildly compressible Euler equations that relies on a linear or nonlinear indicator function to identify the regions of the domain where artificial viscosity is needed and determine its amount. For the realization of this technique, we adopt a three step algorithm called Evolve-Filter-Relax (EFR), which at every time step evolves the solution (i.e., solves the Euler equations on a coarse mesh), then filters the computed solution, and finally performs a relaxation step to combine the filtered and non-filtered solutions. We show that the EFR algorithm is equivalent to an eddy-viscosity model in Large Eddy Simulation. Three indicator functions are considered: a constant function (leading to a linear filter), a function proportional to the norm of the velocity gradient (recovering a Smagorinsky-like model), and a function based on approximate deconvolution operators. Through well-known benchmarks for atmospheric flow, we show that the deconvolution-based filter yields stable solutions that are much less dissipative than the linear filter and the Samgorinsky-like model and we highlight the efficiency of the EFR algorithm.

math.NA↗
arXiv2023

Applicable Methodologies for the Mass Transfer Phenomenon in Tumble Dryers: A Review

Tumble dryers offer a fast and convenient way of drying textiles independent of weather conditions and therefore are frequently used in ordinary households. However, artificial drying of textiles consumes considerable amounts of energy, approximately 8.2 percent of the residential electricity consumption is for drying of textiles in northern European countries (Cranston et al., 2019). Several authors have investigated the aspects of the clothes drying cycle with experimental and numerical methods to understand and improve the process. The first turning point study on understanding the physics of evaporation for tumble dryers was presented by Lambert et al. (1991) in the early 90s. With the aid of Chilton_Colburn analogy, they introduced the concept of area-mass transfer coefficient to address evaporation rate. Afterwards, several experimental or numerical studies were published based on this concept, and furthermore, the model was then developed into 0-dimensional (Deans, 2001) and 1-dimensional (Wei et al., 2017) to gain more accuracy. The evaporation rate is considered to be the main system parameter for dryers with which other performance parameters including drying time, effectiveness, moisture content and efficiency can be estimated. More recent literature focused on utilizing dimensional analysis or image processing techniques to correlate drying indices with system parameters. However, the validity of these regressed models is machine-specific, and hence, cannot be generalized yet. All the previous models for estimating the evaporation rate in tumble dryers are discussed. The review of the related literature showed that all of the previous models for the prediction of the evaporation rate in the clothes dryers have some limitations in terms of accuracy and applicability.

math.NA↗