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=12f82dcaba04c4a7c44f8e5b20101997