Nonlinear model order reduction based on local reduced‐order bases

By David Amsallem, Matthew J. Zahr, Charbel Farhat. 2012

521 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1acffa65a20e17805705f0847f184b2a73105019

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In Computational Mechanics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Improving the efficiency of large scale topology optimization through on‐the‐fly reduced order model construction (2015, background): “They have gained much interest in recent years in various domains, be it in analysis [4]-[7] or optimization [8]-[11].”
Machine Learning for Fluid Mechanics (2019, methodology): “In Amsallem et al. (2012) k -means clustering was used to partition phase space into separate regions, in which local reduced-order bases were constructed, resulting in improved stability and robustness to parameter variations.”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, background): “Other approaches pursue the use of multiple linear subspaces instead of employing a single global linear trial subspace; these local subspaces can be tailored to different regions of the time domain [24, 22], physical domain [71], or state space [2, 60].”
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency (2014, background): “The integration of the concept of local reduced-order bases [51] into the overall nonlinear model reduction methodology described in this paper and its equally successful application to nonlinear parametric applications are the subject of a companion paper.”
A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs (2020, methodology): “5 [8, 8, 32] [16, 16, 16] [5, 5] 16 2 SAME”
Evaluation of aerodynamic loads via reduced order methodology (2015, background): “Some recent pertinent examples in the context of aeroelasticity for helicopter rotor blades can be found in [25,26], whereas a first attempt to address the entire aerodynamic field around a rotor via modal ROM is presented in [27].”
Data-driven reduced order modeling for time-dependent problems (2019, methodology): “the RB method for linear evolution equations [16], the POD-based reduced-order fluid/structure modeling [24], the nonlinear ROM based on local reduced-order bases [3], the dynamic mode decomposition [21], several developments of the RB method for complex models [22, 34, 40], recently proposed struct”
Structure‐preserving, stability, and accuracy properties of the energy‐conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models (2015, background): “For problems characterized by different physical regimes, moving features, discontinuities, or fronts, the solution space can be partitioned into sub-regions that characterize the nonlinear features of the solution of interest, and a local ROB V can be constructed off-line and assigned to each sub-r”
Interpolation-based reduced-order modelling for steady transonic flows via manifold learning (2014, background): “This may be compared to the localisation strategies proposed by Amsallem, Zahr, and Farhat (2012) and Peherstorfer et al. (2014).”
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems (2018, unknown): “his section, we assume that the fractional order α in the model (4.1) is unknown. Thus the purpose is to recover is Z = (Z0,Z1,α) ∈ R3. We set a uniform prior for Z = (Z0,Z1,α) on the parameter space [0,1]3. To generate data for the inversion, the ‘true’ parameter is choose to be (Z0 = 0.25,Z1 = 0.7”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “Recent work has proposed approaches to split Ω into multiple subdomains and construct reduced models in each subdomain [10, 76, 82, 121, 190, 221].”
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem (2015, unknown): “…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].”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, methodology): “Data-driven approaches have been used to characterize turbulent systems [9], including clustering [90], network theory [91], [92], DMD-based model reduction [93], [94], and local POD subspaces [95], to name a few.”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “Localization methods have been successfully pursued to mitigate the modal deformation of the POD basis by partitioning the state space, 164–167 time domain, 157,168–175 physical domain, 176–179 or parameter space 180–182 using multiple local, piecewise afﬁne subspace approximations instead of a…”