Two-Body and Three-Body Interaction Potentials. After computing the two-body interaction 𝑊 ! (𝑑 4! ) and the three-body contribution ∆𝑊 % (𝑑 4! , 𝑑 4% , 𝑑 !% ) from simulations, the two data sets were individually fitted to the PIP potentials specified in Eqs. 3 and 6. The unknown parameters in the PIPs were obtained through a combination of singular value decomposition and simplex optimization minimizing the mean square error between PIP-predicted and computed potentials using Tikhonov regularization. The two-body interactions were computed at 120 distinct values of 𝑑 4! in the range 6𝜎 and 14𝜎, using finer spacings at 𝑑 4! ≤ 8𝜎 where it exhibits sharper variations. Figure presents a representative two-body PMF (red circles, Fig. ) for polymer-grafted NPs at grafting density