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Joachim Bona-Pellissier

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#machine learning Preprint Sep 2026

Fast Learning Rates for Physics-Informed Kernel Methods

This work considers the setting where $D$ is a linear differential operator and analyzes a physics-informed kernel estimator combining value observations and differential observations to derive physically consistent rates in a stronger norm that jointly controls the errors in $\hat u$ and $D\hat u$.

Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti et al. · 0 citations

Jul 2026

PIKS: Universal Physics-Informed Kernel Methods

The universal consistency of PIKS is established for linear differential constraints, proving that for universal kernels (such as Gaussian or Mat\'ern), the estimator asymptotically learns the target while satisfying physical constraints.

Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria et al. · arXiv.org · 1 citation