Randomized Algorithms for Non-Intrusive Parametric Reduced Order Modeling

This paper demonstrates the development of purely data-driven, nonintrusive parametric reduced-order models for the emulation of high-dimensional field outputs using randomized linear algebra techn...

[1]  M. Fossati.  Evaluation of aerodynamic loads via reduced order methodology , 2015 .

[2]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[3]  Ionel M. Navon,et al.  Non-intrusive reduced order modelling of the Navier-Stokes equations , 2015 .

[4]  Benjamin Peherstorfer,et al.  Projection-based model reduction: Formulations for physics-based machine learning , 2019, Computers & Fluids.

[5]  Nathan Halko,et al.  Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions , 2009, SIAM Rev..

[6]  H. Tran,et al.  Modeling and control of physical processes using proper orthogonal decomposition , 2001 .

[7]  V. Ralph Algazi,et al.  On the optimality of the Karhunen-Loève expansion (Corresp.) , 1969, IEEE Trans. Inf. Theory.

[8]  P. Nair,et al.  Reduced‐order modeling of parameterized PDEs using time–space‐parameter principal component analysis , 2009 .

[9]  J. Hesthaven,et al.  Greedy Nonintrusive Reduced Order Model for Fluid Dynamics , 2018, AIAA Journal.

[10]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[11]  Kathrin Smetana,et al.  Randomized Local Model Order Reduction , 2017, SIAM J. Sci. Comput..

[12]  D. MacManus,et al.  Correction: Aerodynamic interference on a finned slender body , 2016 .

[13]  Christopher C. Pain,et al.  Non-intrusive reduced order modelling of fluid–structure interactions , 2016 .

[14]  Joaquim R. R. A. Martins,et al.  Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark , 2015 .

[15]  Karen Willcox,et al.  Surrogate Modeling Approach to Support Real-Time Structural Assessment and Decision Making , 2015 .

[16]  C. Pain,et al.  Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation , 2015 .

[17]  C. Bach,et al.  Randomized low‐rank approximation methods for projection‐based model order reduction of large nonlinear dynamical problems , 2019, International Journal for Numerical Methods in Engineering.

[18]  D. A. Bistrian,et al.  Randomized dynamic mode decomposition for nonintrusive reduced order modelling , 2016, 1611.04884.

[19]  J. Hesthaven,et al.  Data-driven reduced order modeling for time-dependent problems , 2019, Computer Methods in Applied Mechanics and Engineering.

[20]  Lawrence Sirovich,et al.  Karhunen–Loève procedure for gappy data , 1995 .

[21]  Levent Burak Kara,et al.  A data-driven investigation and estimation of optimal topologies under variable loading configurations , 2016, Comput. methods Biomech. Biomed. Eng. Imaging Vis..

[22]  K. Willcox,et al.  Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition , 2004 .

[23]  P. Nair,et al.  Nonintrusive reduced‐order modeling of parametrized time‐dependent partial differential equations , 2013 .

[24]  Jan S. Hesthaven,et al.  Non-intrusive reduced order modeling of nonlinear problems using neural networks , 2018, J. Comput. Phys..

[25]  D. A. Bistrian,et al.  Efficiency of randomised dynamic mode decomposition for reduced order modelling , 2018 .