Name
Title | ||
|---|---|---|
Parametric domain decomposition for accurate reduced order models: Applications of MP-LROM methodology. |
Abstract | ||
|---|---|---|
The multivariate predictions of local reduced-order-models (MP-LROM) methodology, recently proposed by the authors Moosavi et al. (0000), uses machine learning based regression methods to predict the errors of reduced-order models. This study considers two applications of MP-LROM. First, the error model is used in conjunction with a greedy sampling algorithm to generate decompositions of one dimensional parametric domains with overlapping regions, such that the associated local reduced-order models meet the prescribed accuracy requirements. Once a parametric domain decomposition is constructed, any parametric configuration belongs to (at least) one of the partitions; the local reduced-order model associated with that partition approximates the full order model at the given parameters within an accuracy level that is estimated a-priori. The parameter domain decomposition creates a database of the available local bases, local reduced-order, and high-fidelity models, and identifies the most accurate solutions for an arbitrary parametric configuration. Next, this database is used to enhance the accuracy of the reduced-order models using: (1) Lagrange interpolation of reduced bases in the matrix space; (2) Lagrange interpolation of reduced bases in the tangent space of the Grassmann manifold; (3) concatenation of reduced bases followed by a Gram–Schmidt orthogonalization process; and (4) Lagrange interpolation of high-fidelity model solutions. Numerical results with a viscous Burgers model illustrate the potential of the MP-LROM methodology to improve the design of parametric reduced-order models. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2017.11.018 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
Local reduced-order models,Proper Orthogonal Decomposition,Regression machine learning techniques,Interpolation methods,Grassmann manifold | Applied mathematics,Lagrange polynomial,Mathematical optimization,Matrix (mathematics),Parametric statistics,Concatenation,Grassmannian,Orthogonalization,Domain decomposition methods,Mathematics,Tangent space | Journal |
Volume | ISSN | Citations |
340 | 0377-0427 | 1 |
PageRank | References | Authors |
0.36 | 10 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Razvan Stefanescu | 1 | 31 | 6.01 |
| Azam S. Zavar Moosavi | 2 | 14 | 4.12 |
| Adrian Sandu | 3 | 325 | 58.93 |