Integration-free kernels for equivariant Gaussian fields with application in dipole moment prediction

We develop a Gaussian Process model for accurate prediction of the dipole moments of water molecules by incorporating their equivariance under rotations. While kernels guaranteeing such equivariances have been investigated in previous work, their evaluation is often computationaly prohibitive due to required integrations over the involved groups. In this work, we propose an alternative integration-free construction for equivariant kernels, relying on fundamental domain ideas previously explored in the scalar-valued invariant case, establishing a data-efficient and computationally lightweight GP model for dipole moments.