Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

By Toni Lassila, Andrea Manzoni, Alfio Maria Quarteroni, Gianluigi Rozza. 2014

291 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c29a325fcf4e0abb1eec28c78fe64d4c3388bb04

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Citations in the corpus

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets (2021, unknown): “This challenge has motivated a growing literature on reduced-order methods [3, 4, 5, 6, 7, 8, 9] that leverage existing data-sets to build fast emulators, often at the price of reduced accuracy, stability, and generalization performance [10, 11].”
An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows (2014, background): “In fact, this problem arises in several fluid flows applications; its rapid and reliable solution represents a remarkable challenge for a ROM, because of nonlinearities, stability and efficiency issues [16].”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “Usually, constructing ROMs involves dimensionality reduction that attempts to capture the most important dynamical characteristics of often large, high-fidelity simulations and models of physical systems (e.g., in fluid dynamics [145]).”
POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations (2016, methodology): “A viable solution is to employ Reduce Order Modelling (ROM) techniques [6].”
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data (2019, background): “Although holding some promises, the current projection-based ROM techniques have had limited impact on complex fluid dynamic problems mainly because of the stability and robustness issues [4, 5].”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “Usually, constructing ROMs involves dimensionality reduction that attempts to capture the most important dynamical characteristics of often large, high-fidelity simulations and models of physical systems (e.g., in fluid dynamics [164]).”
Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, methodology): “At least two approaches in the construction stage of the RB can be pursued: greedy algorithms and POD [1].”