Fast Learning Rates for Physics-Informed Kernel Methods
In physics-informed machine learning, a target function $u^*$ is learned from noisy value observations $y_i=u^*(x_i)+ \varepsilon_i$, together with differential information, given either by noisy observations $d_j=(Du^*)(z_j)+ξ_j$ or by a known physical constraint $Du^*=v$. We consider the setting where $D$ is a linear differential operator and analyze a physics-informed kernel estimator $\hat u$ combining $n$ value observations and $m$ differential observations. In this context, we ask how much can differential information improve predictions, and how does this improvement depend quantitatively on $n$, $m$, and $D$. We prove finite-sample bounds, supported by numerical simulations, revea...
| Authors | Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti et al. |
|---|---|
| Primary category | stat.ML |
| Published | 16 September 2026 |
| Last updated at source | 16 September 2026 |
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