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

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

Aeroacoustic Reduced-Order Models Based on a priori/posteriori Data Analysis

Two Reduced-Order Models for the simulation of aeroacoustic phenomena are presented. One model is based on Proper Orthogonal Decomposition, relying on a posteriori analysis of a set of high-delity calculations, the snapshots in the parametric space. To partially reduce the number of necessary snapshots, a self-adaptive sampling technique is proposed. Instead of a regular and homogeneous one-step sampling, a gradual and optimised enhancement of the sample set is dened. The second model is based on Proper Generalized Decomposition, which can be viewed as a a-priori approach, able to build the reduced-order approximation without relying on the knowledge of the solution of the complete problem, assessing the model accuracy and, if necessary, to enrich the reduced approximation basis. Both methods are applied to the computation of scattering of sound by a circular cylinder