Nonlinear Model Reduction via Discrete Empirical Interpolation

By Saifon Chaturantabut, Danny C. Sorensen. SIAM Journal on Scientific Computing, 2010

2,035 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a0085c2257dede6fd40a46d473b30d4f81dcab08

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Citations in the corpus

Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “The reduced model f (3) is derived as f (2) except that the nonlinear function g is approximated by the discrete empirical interpolation method (DEIM) [12] as described in [51].”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, positive): “Among this class of methods, the missing point estimation [19] and Gauss Newton with approximated tensors (GNAT) [66] methods both build upon the gappy POD interpolation method [87]; the empirical interpolation method (EIM) [26] and its discrete variant, the discrete empirical interpolation method (”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “Connections of the method to the so-called discrete EIM (DEIM) are derived and we show that we obtain the same results with less run-time complexity, allowing now to apply the EIM error estimators to both methods.”
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem (2015, positive): “…methods were developed using the Petrov–Galerkin projection for reducing the dimension of a discrete nonlinear dynamic computational model, see e.g. Hyper-reduction method [13,14], Gauss–Newton with Approximation Tensor (GNAT) method [14–16] or Discrete Empirical Interpolation (DEIM) method [9,17].”
Nonlinear model order reduction based on local reduced‐order bases (2012, methodology): “A second class of hyper reduction techniques are based on the concept of empirical interpolation [20,21]—also known in its discrete form as the Gappy POD technique [6,20,26]—or the related discrete empirical interpolation method [5].”
On the use of modal derivatives for nonlinear model order reduction (2016, methodology): “Probably, the most popular choice for such a method is the discrete empirical interpolation method (DEIM) [37, 38].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “There are some techniques, which provide efﬁcient estimates of f ( V z ( t )) as the (discrete) empirical interpolation methods (DEIM or EIM) [21,57], the missing point estimation method [8], or a best points interpolation method [147].”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[240] S.”
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, methodology): “Chaturantabut and Sorensen [23] proposed a non-linear model reduction via the discrete empirical interpolation method (DEIM) [25] [26], which is the discrete version of the empirical interpolation method (EIM) [24].”
Non-intrusive reduced order modeling of nonlinear problems using neural networks (2018, methodology): “Without escaping the algebraic framework, this can be overcome by resorting to suitable techniques such as the discrete empirical interpolation method (DEIM) [10] or its matrix variant (MDEIM) [37], aiming at recovering an affine dependency on the parameter µ.”
A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models (2017, methodology): “caveat is remedied by equipping an MOR method with a rigorous procedure for approximating the resulting reduced operators whose computational complexity scales only with the small size n of the ROM [2, 4, 13, 14].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “POD is a popular basis generation method because it applies to a wide range of problems, including time-dependent and nonlinear problems [39, 91, 119, 120, 186].”
Multifidelity importance sampling (2016, methodology): “The nonlinear term is approximated using DEIM [43, 45], where the DEIM basis is generated by applying POD to the nonlinear reaction source term evaluated at the 2500 snapshots.”
A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs (2020, positive): “The same difficulty may also affect hyper-reduction techniques, such as the (discrete) empirical interpolation method [8,16].”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, neutral): “63,216,217 Examples of hyperreduction include the empirical interpolation method (EIM), 86 its discrete version (DEIM), 90,218 the gappy POD, 100,111,219 and the missing point estimation (MPE), 108,220 where the approximation is performed using sampling techniques.”