We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called "quasi-PDFs," can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized nonperturbatively in the RI/MOM-scheme. However, the recent renormalized quasi-PDFs suffer from unphysical oscillations that alter the shape of the true distribution as a function of Bjorken-x. In this paper, we propose two possible solutions to overcome this problem and demonstrate the efficacy of the methods on the 2 + 1 + 1-flavor lattice data at physical pion mass with lattice spacing 0.09 fm and volume (5.76 fm)(3).