Multi-Fidelity Extension to Non-Intrusive Proper Orthogonal Decomposition Based Surrogates

Abstract

This paper presents a methodology for building multi-fidelity surrogate models based on Non-Intrusive Proper Orthogonal Decomposition. The proposed strategy aims at fusing multiple fidelity levels of simulation to improve the quality of surrogate models exploited in automated optimization loops of industrial-scale problems. A proof of concept is then given on a mathematical toy example which illustrates the ability of the proposed method to significantly reduce the overall computation cost. A 3D industrial study of a 1.5 stage booster is then presented to address the scaling capability of the proposed methodology.

Multi-fidelity non-intrusive reduced-order modelling based on manifold alignment

“…A multi-fidelity regression model is then used to combine the high-and low-fidelity latent variables. -Extended POD [25]: The POD basis of the low-fidelity results is projected onto the null space of the POD basis of the high-fidelity results to extend the latter. The extended basis is then used to compute the high-and low-fidelity results that are both used to train a multi-fidelity regression model.…”

“…Furthermore, the above datasets all use grids of different sizes, and thus, have inconsistent dimensionality. Other multi-fidelity ROM methods would require a pre-processing step where all the solutions would be mapped onto a common grid, usually the coarser one [25][26][27]. However, with the MA-ROM method, these results are combined into a single model without additional manipulations of the results.…”

“…before building the ROM. This strategy was used by Benamara et al [25,26], who performed CFD simulations of a compressor blade using a coarse and fine grid, then interpolated all the results onto the coarse grid. In their work, they extracted an initial POD basis using the high-fidelity solution and then extended this subspace using basis vectors obtained from the low-fidelity solutions.…”

Development of a Multi-Fidelity Reduced-Order Model Based on Manifold Alignment

“…An alternative solution is to map the results of all fidelity levels onto a common grid during a pre-processing step, i.e., before building the ROM. This strategy was used by Benamara et al [18,19] who performed CFD simulations of a compressor blade using a coarse and fine grid, then interpolated all the results onto the coarse grid. In their work, they extracted an initial POD basis using the high-fidelity solution and then extended this subspace using basis vectors obtained from the low-fidelity solutions.…”

“…Furthermore, the above datasets all use grids of different sizes, and thus, have inconsistent dimensionality. Other multi-fidelity ROM methods would require a pre-processing step where all the solutions would be mapped unto a common grid, usually the coarser one [18][19][20]. However, with the MA-ROM method, these results are combined into a single model without additional manipulations of the results.…”