@article {2022, title = {The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {392}, year = {2022}, abstract = {

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. {\textcopyright} 2022 Elsevier B.V.

}, keywords = {Advection, Computational complexity, Deep neural network, Deep neural networks, Linear subspace, Multiphase simulations, Non linear, Nonlinear hyperbolic equation, Partial differential equations, Phase space methods, Pre-processing, Principal component analysis, reduced order modeling, Reduced order modelling, Reduced-order model, Shifted-POD}, doi = {10.1016/j.cma.2022.114687}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633\&doi=10.1016\%2fj.cma.2022.114687\&partnerID=40\&md5=12f82dcaba04c4a7c44f8e5b20101997}, author = {Davide Papapicco and Nicola Demo and Michele Girfoglio and Giovanni Stabile and Gianluigi Rozza} } @conference {2022, title = {A Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks}, booktitle = {2022 IEEE International Conference on Image Processing (ICIP)}, year = {2022}, doi = {10.1109/ICIP46576.2022.9897513}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @booklet {2021, title = {A Dimensionality Reduction Approach for Convolutional Neural Networks}, year = {2021}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @article {2021, title = {A dynamic mode decomposition extension for the forecasting of parametric dynamical systems}, journal = {arXiv preprint arXiv:2110.09155}, year = {2021}, author = {Francesco Andreuzzi and Nicola Demo and Gianluigi Rozza} } @article {2021, title = {An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques}, journal = {Bolletino dell Unione Matematica Italiana}, volume = {14}, year = {2021}, pages = {211-230}, abstract = {

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{\textemdash}especially dealing with complex industrial geometries{\textemdash}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.

}, doi = {10.1007/s40574-020-00263-4}, author = {Nicola Demo and Giulio Ortali and Gianluca Gustin and Gianluigi Rozza and Gianpiero Lavini} } @unpublished {2021, title = {AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS}, year = {2021}, author = {Nicola Demo and Maria Strazzullo and Gianluigi Rozza} } @article {2021, title = {Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing}, journal = {Journal of Marine Science and Engineering}, volume = {9}, year = {2021}, pages = {185}, abstract = {

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.

}, issn = {2077-1312}, doi = {10.3390/jmse9020185}, url = {https://www.mdpi.com/2077-1312/9/2/185}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {2020, title = {A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems}, journal = {SIAM Journal on Scientific Computing}, volume = {43}, year = {2021}, chapter = {B831}, abstract = {

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 {\textendash} Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov {\textendash} and finally we apply it to an aeronautical shape optimization problem.

}, doi = {https://doi.org/10.1137/20M1345219}, url = {https://arxiv.org/abs/2006.07282}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @conference {2020, title = {Advances in reduced order methods for parametric industrial problems in computational fluid dynamics}, booktitle = {Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018}, year = {2020}, abstract = {

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.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686\&partnerID=40\&md5=fb0b1a3cfdfd35a104db9921bc9be675}, author = {Gianluigi Rozza and M.H. Malik and Nicola Demo and Marco Tezzele and Michele Girfoglio and Giovanni Stabile and Andrea Mola} } @article {2020, title = {Enhancing CFD predictions in shape design problems by model and parameter space reduction}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {7}, year = {2020}, abstract = {

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.

}, doi = {https://doi.org/10.1186/s40323-020-00177-y}, url = {https://arxiv.org/abs/2001.05237}, author = {Marco Tezzele and Nicola Demo and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @article {2020, title = {Reduced order isogeometric analysis approach for pdes in parametrized domains}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {137}, year = {2020}, pages = {153-170}, abstract = {

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.

}, doi = {10.1007/978-3-030-48721-8_7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035\&doi=10.1007\%2f978-3-030-48721-8_7\&partnerID=40\&md5=7b15836ae65fa28dcfe8733788d7730c}, author = {Fabrizio Garotta and Nicola Demo and Marco Tezzele and Massimo Carraturo and Alessandro Reali and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

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 {\textemdash} assuming the topology is inaltered by the deformation {\textemdash}, 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.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565\&partnerID=40\&md5=d76b8a1290053e7a84fb8801c0e6bb3d}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {

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 {\textendash}- assuming the topology is inaltered by the deformation {\textendash}-, 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.

}, url = {https://arxiv.org/abs/1905.05982}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {2019, title = {A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces}, journal = {Comptes Rendus - Mecanique}, volume = {347}, year = {2019}, pages = {873-881}, abstract = {

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions{\textemdash}computed for properly chosen parameters, using a full-order model{\textemdash}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){\textemdash}a data-driven reduced order method{\textemdash}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.

}, doi = {https://doi.org/10.1016/j.crme.2019.11.012}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471\&doi=10.1016\%2fj.crme.2019.11.012\&partnerID=40\&md5=dcb27af39dc14dc8c3a4a5f681f7d84b}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @conference {2019, title = {Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

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.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244\&partnerID=40\&md5=3e1f2e9a2539d34594caff13766c94b8}, author = {Marco Tezzele and Nicola Demo and Gianluigi Rozza} }