Graph Laplacian-based spectral multi-fidelity modeling

• Published in: Scientific reports Vol. 13; no. 1; p. 16618
• Main Authors: Pinti, Orazio, Oberai, Assad A
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group 03.10.2023; Nature Publishing Group UK; Nature Portfolio
• Subjects: Accuracy; Approximation; Datasets; Fluid mechanics; Methods; Neural networks
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-023-43719-1

Low-fidelity data is typically inexpensive to generate but inaccurate, whereas high-fidelity data is accurate but expensive. To address this, multi-fidelity methods use a small set of high-fidelity data to enhance the accuracy of a large set of low-fidelity data. In the approach described in this paper, this is accomplished by constructing a graph Laplacian from the low-fidelity data and computing its low-lying spectrum. This is used to cluster the data and identify points closest to the cluster centroids, where high-fidelity data is acquired. Thereafter, a transformation that maps every low-fidelity data point to a multi-fidelity counterpart is determined by minimizing the discrepancy between the multi- and high-fidelity data while preserving the underlying structure of the low-fidelity data distribution. The method is tested with problems in solid and fluid mechanics. By utilizing only a small fraction of high-fidelity data, the accuracy of a large set of low-fidelity data is significantly improved.