Nan-Hong Kuo, Renata Wong
We establish a mathematical equivalence between Support Vector Machine (SVM) kernel functions and quantum propagators represented by time-dependent Green's functions, which has remained largely unexplored. We demonstrate that many common SVM kernels correspond naturally to Green's functions via operator inversion theory. The sigmoid kernel does not always satisfy Mercer's theorem, and therefore the corresponding Green's function may also fail to perform optimally. We further introduce a Kernel Polynomial Method (KPM) for designing customized kernels that align with Green's functions. Our numerical experiments confirm that employing positive-semidefinite kernels that correspond to Green's functions significantly improves predictive accuracy of SVM models in physical systems.