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<p>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.</p>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=12f82dcaba04c4a7c44f8e5b2010199700617nas a2200133   4500008004100000245014100041210006900182100002200251700001700273700002300290700002200313700002100335856012700356       2021                        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 1 aPapapicco, Davide1 aDemo, Nicola1 aGirfoglio, Michele1 aStabile, Giovanni1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/neural-network-shifted-proper-orthogonal-decomposition-machine-learning-approach-non01894nas 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<p>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.</p>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=dcb27af39dc14dc8c3a4a5f681f7d84b