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Fast Learning Rates for Physics-Informed Kernel Methods

Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.

The paper analyzes a physics-informed kernel estimator combining n value observations and m differential observations for a linear differential operator D, asking how much differential information improves prediction. The authors prove finite-sample bounds, supported by simulations, revealing a two-regime structure: when m is limited the rate depends jointly on n and m, and when m exceeds a problem-dependent threshold the rate saturates to the oracle rate. Examples in Sobolev spaces, including partial Laplacian constraints on the torus and gradient observations on bounded domains, illustrate improvements from the nonparametric n^-1/4 rate to the parametric n^-1/2 rate, plus physically consistent rates in a stronger norm.

arXiv cs.AI / cs.LG / cs.CL · 20h agoAI research

Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion

VyPER framework reconstructs collider events using hypergraph representation learning and graph-conditioned diffusion, outperforming existing reconstruction techniques across Standard Model processes.

Researchers present VyPER, a geometric learning framework that represents collider events as hypergraphs with a physics-inspired topology for particle event reconstruction. It combines supervised hyperedge classification for assigning measured jets and charged leptons to parent particles with a graph-conditioned diffusion model predicting unmeasured neutrino kinematics, optimized with a joint loss. Evaluated across several proton-proton collision processes, it demonstrates accurate reconstruction across Higgs, electroweak, and top-quark sectors.

arXiv cs.AI / cs.LG / cs.CL · 19h agoAI research