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Data-Driven Extrapolation Via Feature Augmentation Based on Variably Scaled Thin Plate Splines

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Abstract

The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our attention towards kernel models that have the advantage of being meshfree. Precisely, the proposed numerical method makes use of the so-called Variably Scaled Kernels (VSKs), which are introduced to implement a feature augmentation-like strategy based on discrete data. Due to the possible uncertainty on the data and since we are interested in modelling the behaviour of the target functions, we seek for a regularized solution by ridge regression. Focusing on polyharmonic splines, we investigate their implementation in the VSK setting and we provide error bounds in Beppo–Levi spaces. The performances of the method are then tested on functions showing exponential or rational decay. Comparisons with Support Vector Regression (SVR) are also carried out and highlight that the proposed approach is effective, particularly since it does not require to train complex architecture constructions.

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Notes

  1. Tests have been carried out on a Intel(R) Core(TM) i7 CPU 4712MQ 2.13 GHz processor.

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Acknowledgements

This research has been accomplished within the Research ITalian network on Approximation (RITA) and partially funded by the ASI - INAF grant “Artificial Intelligence for the analysis of solar FLARES data (AI-FLARES)”. The authors are members of the GNCS IN\(\delta \)AM Research group. We sincerely thank the reviewers for helping us to significantly improve the manuscript

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Authors and Affiliations

  1. Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”, Caserta, Italy

    Rosanna Campagna

  2. CNR-SPIN, Via Dodecaneso 33, 16146, Genova, Italy

    Emma Perracchione

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  1. Rosanna Campagna
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  2. Emma Perracchione
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Correspondence to Rosanna Campagna.

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Campagna, R., Perracchione, E. Data-Driven Extrapolation Via Feature Augmentation Based on Variably Scaled Thin Plate Splines. J Sci Comput 88, 15 (2021). https://doi.org/10.1007/s10915-021-01526-8

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  • DOI: https://doi.org/10.1007/s10915-021-01526-8

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