Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations

By Kevin T. Carlberg, Charbel Bou-Mosleh, Charbel Farhat. 2011

714 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3095256996f8883797190cfc28c3f2912d2c3426

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows (2012, neutral): “[1]) is to decrease this computational cost.”
A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics (2017, methodology): “The following terminology is borrowed from [41] and adopted in this section:”
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, methodology): “introduced the Petrov–Galerkin method to control the stability of reduced order modelling of a 1D nonlinear static problem [32,33].”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, methodology): “This includes the reduced-basis technique [62, 67] and proper orthogonal decomposition (POD) [37, 15] for parameterized stationary problems; balanced truncation [54], rational interpolation [4, 32], and Craig–Bampton model reduction [20] for linear time invariant (LTI) systems; and Galerkin projecti”
High-performance model reduction techniques in computational multiscale homogenization (2014, background): “Generally speaking, a reduced basis approximation is said to be consistent if, in the limit of no truncation, it introduces no additional error in the solution of the same problem for which the data used in constructing the basis functions were acquired [14].”
Nonlinear model order reduction based on local reduced‐order bases (2012, methodology): “The GNAT (Gauss–Newton with approximated tensor quantities) method introduced in [6, 7] falls within this class of methods.”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “” There are myriad complex systems that would benefit from principled, scalable sensor and actuator placement, in cluding fluid flow control [9], power grid optimization [10], epidemiological modeling and suppression [11], bioregulatory network monitoring and control [12], and high-performance compu”
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, methodology): “Related or similar approaches have been developed specifically for hyper reduction at the semidiscrete [22, 23] and fully discrete [10, 11, 24, 25] levels.”