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We propose a structure-preserving kernel ridge regression method for learning elastic potentials on Lie groups from noisy observations of force and torque fields. The approach is demonstrated on the special Euclidean group SE(3), where the elastic potential acts as an external control. A key advantage of our method is that the potential function estimator admits a globally defined closed-form solution, with provable convergence analysis. Numerical experiments confirm the effectiveness of the proposed scheme.

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A Kernel-Based Global Method for the Learning of Elastic Potentials on Lie Groups

  • 会议论文

  • 发表日期：

    2026年

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  • Domenico Campolo,
  • Jianyu Hu,
  • Juan-Pablo Ortega,
  • Daiying Yin

摘要

We propose a structure-preserving kernel ridge regression method for learning elastic potentials on Lie groups from noisy observations of force and torque fields. The approach is demonstrated on the special Euclidean group SE(3), where the elastic potential acts as an external control. A key advantage of our method is that the potential function estimator admits a globally defined closed-form solution, with provable convergence analysis. Numerical experiments confirm the effectiveness of the proposed scheme.