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arXiv · 2304.04862

A few-shot graph Laplacian-based approach for improving the accuracy of low-fidelity data

Orazio Pinti·Assad A. Oberai
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Abstract

Low-fidelity data is typically inexpensive to generate but inaccurate. On the other hand, high-fidelity data is accurate but expensive to obtain. 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 using the low-fidelity data and computing its low-lying spectrum. This spectrum is then used to cluster the data and identify points that are closest to the centroids of the clusters. High-fidelity data is then acquired for these key points. Thereafter, a transformation that maps every low-fidelity data point to its bi-fidelity counterpart is determined by minimizing the discrepancy between the bi- and high-fidelity data at the key points, and to preserve the underlying structure of the low-fidelity data distribution. The latter objective is achieved by relying, once again, on the spectral properties of the graph Laplacian. This method is applied to a problem in solid mechanics and another in aerodynamics. In both cases, this methods uses a small fraction of high-fidelity data to significantly improve the accuracy of a large set of low-fidelity data.

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Orazio Pinti, Assad A. Oberai. 2023-03-29. A few-shot graph Laplacian-based approach for improving the accuracy of low-fidelity data. https://arxiv.org/abs/2304.04862

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