Efficiency of approximate PIKS algorithms

Establish whether approximate algorithms for Physics Informed Kernel MethodS that are more computationally efficient than the exact kernel solver can preserve the statistical learning gains proved for the exact estimator.

Background

The exact PIKS estimator has a finite-dimensional kernel representation but requires solving a system with computational costs that scale cubically in the combined number of value and differential observations. The paper asks whether more efficient approximate procedures can retain the improved statistical rates resulting from differential information, rather than sacrificing the theoretical gains for computational efficiency.