Reproduce “Fast Learning Rates for Physics-Informed Kernel Methods” on OpenResearch
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About this paper
Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti, Lorenzo Rosasco
PIKS fits noisy values and derivatives with an RKHS smoothness penalty. Its root-mean-square value-prediction error, defined as the square root of expected squared error on a fresh value-distributed input, has a high-probability bound under A1–A6: up to logarithmic factors, n^-1/4m^-(1-r)/8 below m_crit and n^-[1/(2(1+α))] above it. For gradients, α=0, m_crit is at least n^2, and invisible directions remain value-limited.
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