A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

By Peter Benner, Serkan Gugercin, Karen E. Willcox. SIAM Review, 2015

1,985 citations recorded by the source corpus.

United States. Air Force Office of Scientific Research (Computational Mathematics Grant FA9550-12-1-0420)

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7f4c00eec8cb42aec2bfaf0effb5c87b66202574

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Citations in the corpus

Model Reduction for Flow Analysis and Control (2017, methodology): “Readers are referred to Benner et al. (2015) for a recent review of model reduction methods for linear systems and to Brunton & Noack (2015) for a comprehensive overview of methods used for the control of turbulence.”
Deep learning in fluid dynamics (2017, methodology): “When coupled with Galerkin projection, POD reduction forms the mathematical basis of reduced-order modelling, which provides an enabling strategy for computing high-dimensional discretizations of complex ﬂows (Benner et al. 2015).”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, background): “There are several ways to construct the reduced operators of the reduced model for a parameter µ ∈ D that does not coincide with any of the parameters µ 1 , . . . , µ M [43].”
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data (2019, background): “projection-based reduced order models (ROMs) and data-fit models [2].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “There are a variety of ways to construct the low-dimensional subspace; see [19] for a detailed review.”
Modal Analysis of Fluid Flows: Applications and Outlook (2019, methodology): “ are generally too slow for realtime feedback control. Thus, signicant eort has gone into developing ROMs, with the goal of accurately and eciently reproducing only the most relevant ow mechanisms [74,215]. A classical approach involves Galerkin projection of the governing Navier-Stokes equations on”
Data-driven discovery of coordinates and governing equations (2019, neutral): “[6] This results in a dataset that is a nonlinear combination of the true Lorenz variables, shown in Fig.”
A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs (2020, background): “In particular, in projection-based ROMs, the reduced dynamics is obtained through a projection process onto a linear subspace [9,10,48].”
Digital twin, physics-based model, and machine learning applied to damage detection in structures (2020, background): “To alleviate this last issue, reduced-order models serving as proxies for the original expensive one might be constructed [29, 30, 31].”
Enhancing computational fluid dynamics with machine learning (2021, background): “Lee and Carlberg [105] recently showed that deep convolutional autoencoders may be used to greatly improve the performance of classical ROM techniques based on linear subspaces [106, 107].”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, methodology): “Case p = r : sampling methods such as EIM and QR are practical for sensor placement within a large number of candidate locations in ﬁne spatial grids; hence, they are the methods of choice in reduced-order modeling [143].”
Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “For example, available surrogate models may include projection-based reduced models [44, 43, 24, 3], data-fit interpolation and regression models [21], machine-learning-based support vector machines (SVMs) [16, 48, 11], and simplified-physics models [2, 37].”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[258] P.”