Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases. (English) Zbl 07527732
Summary: Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov \(N\)-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel et al., “Model order reduction assisted by deep neural networks (ROM-net)”, Adv. Model. and Simul. Eng. Sci. 7, Article No. 16, 27 p. (2020; doi:10.1186/s40323-020-00153-6)]. This criterion also provides engineers with a very practical method for ROM-nets’ hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 76Mxx | Basic methods in fluid mechanics |
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