02363nas a2200349 4500008004100000245014100041210006900182490000800251520110500259653001401364653002901378653002401407653002501431653002001456653002701476653001501503653003401518653003501552653002401587653001901611653003301630653002701663653002801690653002401718653001601742100002201758700001701780700002301797700002201820700002101842856015001863 2022 eng d00aThe Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations0 aNeural Network shiftedproper orthogonal decomposition A machine 0 v3923 a

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. © 2022 Elsevier B.V.

10aAdvection10aComputational complexity10aDeep neural network10aDeep neural networks10aLinear subspace10aMultiphase simulations10aNon linear10aNonlinear hyperbolic equation10aPartial differential equations10aPhase space methods10aPre-processing10aPrincipal component analysis10areduced order modeling10aReduced order modelling10aReduced-order model10aShifted-POD1 aPapapicco, Davide1 aDemo, Nicola1 aGirfoglio, Michele1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b2010199700508nas a2200109 4500008004100000245010500041210006900146100002200215700001700237700002100254856012300275 2022 eng d00aA Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks0 aProper Orthogonal Decomposition Approach for Parameters Reductio1 aMeneghetti, Laura1 aDemo, Nicola1 aRozza, Gianluigi uhttps://math.sissa.it/publication/proper-orthogonal-decomposition-approach-parameters-reduction-single-shot-detector-000456nas a2200109 4500008004100000245007400041210006900115100002200184700001700206700002100223856010200244 2021 eng d00aA Dimensionality Reduction Approach for Convolutional Neural Networks0 aDimensionality Reduction Approach for Convolutional Neural Netwo1 aMeneghetti, Laura1 aDemo, Nicola1 aRozza, Gianluigi uhttps://math.sissa.it/publication/dimensionality-reduction-approach-convolutional-neural-networks00494nas a2200109 4500008004100000245009500041210006900136100002500205700001700230700002100247856011600268 2021 eng d00aA dynamic mode decomposition extension for the forecasting of parametric dynamical systems0 adynamic mode decomposition extension for the forecasting of para1 aAndreuzzi, Francesco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://math.sissa.it/publication/dynamic-mode-decomposition-extension-forecasting-parametric-dynamical-systems01866nas a2200169 4500008004100000245014800041210006900189300001200258490000700270520119600277100001701473700001901490700002101509700002101530700002201551856012301573 2021 eng d00aAn efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques0 aefficient computational framework for naval shape design and opt a211-2300 v143 a

This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

1 aDemo, Nicola1 aOrtali, Giulio1 aGustin, Gianluca1 aRozza, Gianluigi1 aLavini, Gianpiero uhttps://math.sissa.it/publication/efficient-computational-framework-naval-shape-design-and-optimization-problems-means00519nas a2200109 4500008004100000245011200041210006900153100001700222700002200239700002100261856012700282 2021 eng d00aAN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS0 aEXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSI1 aDemo, Nicola1 aStrazzullo, Maria1 aRozza, Gianluigi uhttps://math.sissa.it/publication/extended-physics-informed-neural-network-preliminary-analysis-parametric-optimal-control01664nas a2200169 4500008004100000022001400041245011000055210006900165300000800234490000600242520112900248100001701377700001901394700001701413700002101430856004301451 2021 eng d a2077-131200aHull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing0 aHull Shape Design Optimization with Parameter Space and Model Re a1850 v93 a

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.mdpi.com/2077-1312/9/2/18501446nas a2200133 4500008004100000245013900041210006900180490000700249520096200256100001701218700001901235700002101254856003701275 2021 eng d00aA supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems0 asupervised learning approach involving active subspaces for an e0 v433 a

In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

1 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://arxiv.org/abs/2006.0728201497nas a2200169 4500008004100000245010500041210006900146520085900215100002101074700001601095700001701111700001901128700002301147700002201170700001701192856011801209 2020 eng d00aAdvances in reduced order methods for parametric industrial problems in computational fluid dynamics0 aAdvances in reduced order methods for parametric industrial prob3 a

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

1 aRozza, Gianluigi1 aMalik, M.H.1 aDemo, Nicola1 aTezzele, Marco1 aGirfoglio, Michele1 aStabile, Giovanni1 aMola, Andrea uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be67501480nas a2200157 4500008004100000245009400041210006900135490000600204520097900210100001901189700001701208700002201225700001701247700002101264856003701285 2020 eng d00aEnhancing CFD predictions in shape design problems by model and parameter space reduction0 aEnhancing CFD predictions in shape design problems by model and 0 v73 a

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

1 aTezzele, Marco1 aDemo, Nicola1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/2001.0523701572nas a2200181 4500008004100000245008200041210006900123300001200192490000800204520090200212100002201114700001701136700001901153700002301172700002201195700002101217856015201238 2020 eng d00aReduced order isogeometric analysis approach for pdes in parametrized domains0 aReduced order isogeometric analysis approach for pdes in paramet a153-1700 v1373 a

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

1 aGarotta, Fabrizio1 aDemo, Nicola1 aTezzele, Marco1 aCarraturo, Massimo1 aReali, Alessandro1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035&doi=10.1007%2f978-3-030-48721-8_7&partnerID=40&md5=7b15836ae65fa28dcfe8733788d7730c02037nas a2200133 4500008004100000245013800041210006900179520154400248100001701792700001901809700001701828700002101845856003701866 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 a

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0598202116nas a2200133 4500008004100000245013800041210006900179520154200248100001701790700001901807700001701826700002101843856011801864 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 a

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry — assuming the topology is inaltered by the deformation —, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565&partnerID=40&md5=d76b8a1290053e7a84fb8801c0e6bb3d01894nas a2200145 4500008004100000245010300041210006900144300001200213490000800225520130700233100001701540700001901557700002101576856015101597 2019 eng d00aA non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces0 anonintrusive approach for the reconstruction of POD modal coeffi a873-8810 v3473 a

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions—computed for properly chosen parameters, using a full-order model—in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI)—a data-driven reduced order method—with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

1 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471&doi=10.1016%2fj.crme.2019.11.012&partnerID=40&md5=dcb27af39dc14dc8c3a4a5f681f7d84b02446nas a2200121 4500008004100000245014200041210006900183520189700252100001902149700001702168700002102185856011802206 2019 eng d00aShape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces0 aShape optimization through proper orthogonal decomposition with 3 a

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8