A method for interpolating on manifolds structural dynamics reduced‐order models

By David Amsallem, Julien Cortial, Kevin T. Carlberg, Charbel Farhat. 2009

257 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c5ccadf7731c541e0f492bead7c4c1818e3a3be7

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In Civil and Structural Engineering

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Citations in the corpus

Data-driven operator inference for nonintrusive projection-based model reduction (2016, unknown): “,μM via elementwise interpolation [44, 45, 46, 47].”
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows (2012, unknown): “Within these contexts, projection-based model-reduction methods have been successfully applied to problems in structural dynamics [3], aerodynamics [9, 10, 11, 12, 13] and aeroelasticity [14, 15, 16, 17, 18, 19], among others.”
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations (2011, methodology): “…based on data acquisition for multiple conﬁgurations, to interpolation of reduced-order information on suitable manifolds (for example, see [17, 22]), and (3) among these approaches, the most suitable one for adapting the proposed non-linear model reduction method to unsampled conﬁgurations…”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “is proposed by Amsallem and Farhat [2, 1] for efficiently constructing an accurate and robust POD reduced system with respect to parameter variations.”
A physics-informed variational DeepONet for predicting the crack path in brittle materials (2021, background): “This problem has prompted a burgeoning literature on reduced-order approaches [20–22], which use existing data sets to create fast emulators often at the expense of accuracy, stability, and generalization.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “In [3, 4] the ROMs computed at different parameter points were interpolated to obtain a new ROM that was valid also in the intermediate zone between the original parameter points.”
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency (2014, background): “Within this context, projection-based model reduction has been successfully demonstrated in many areas of computational engineering including frequency response analysis [5–7], aeroelastic predictions [8–15], and structural vibrations [16, 17].”
Stabilization of projection‐based reduced‐order models (2012, background): “In particular, it is useful even in the context of a MOR technique with a guaranteed stability, for example, when stable ROMs are interpolated on a manifold [13, 14, 15, 16] for the purpose of adaptation to new model parameter values by an algorithm which does not necessarily preserve the stability ”
An Online Method for Interpolating Linear Parametric Reduced-Order Models (2011, methodology): “which is consistent with the mathematical result established in [21], and stating that the interpolation in a tangent space to the manifold SPD(k) preserves the pattern of a diagonal matrix.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “This idea was recently introduced in [5, 9, 74, 161, 188].”