Interpolation and Quasi-Interpolation Strategies in Data-Driven Reduced Order Models

  • Siena, Pierfrancesco (SISSA)

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Reduced Order Models (ROMs) and surrogate modeling techniques are widely used to efficiently approximate parametric systems, particularly in the context of computationally expensive simulations, including computational fluid dynamics. Interpolation methods, such as Radial Basis Function (RBF) interpolation, as well as regressors and neural networks, are commonly employed in data-driven ROMs to approximate reduced coefficients over the parameter space. However, classical interpolation approaches can exhibit sensitivity to noise in the training data, which can negatively impact prediction accuracy and robustness. In this work, we investigate the role of kernel-based quasi-interpolation as an alternative approximation strategy for noisy datasets. The proposed approach avoids the solution of global linear systems, like RBF, while retaining smoothing properties, making it attractive for data-driven approaches. A comparative study is conducted to assess accuracy, robustness to noise, and sensitivity to some parameters across different approximation strategies. The analysis highlights the trade-offs between interpolation and quasi-interpolation in the presence of noisy data and provides insights into the practical use of kernel-based methods for parametric model reduction.