Here we introduce a distinct ML approach to develop an analytical many-body potential that can accurately describe the two-body and three-body interactions between spherical polymer-grafted NPs in a polymer matrix. The approach involves calculation of PMFs of the NPs in the polymer matrix through CG MD simulations and fitting them using permutationally invariant polynomials cast as functions of Coulomb-transformations of interparticle distances. To validate the developed ML potential, we use it to carry out MD simulations of NPs undergoing assembly and show that all known structural phases, namely, the 1D strings, 2D sheets, and 3D globular aggregates discussed above, are successfully reproduced. The ML potential reduces the computational cost of MD simulations by at least three orders of magnitude, which allowed us to explore NP assembly at large length and time scales and thereby discover additional phases like networks, clusters, and gels that could be assembled from polymer-grafted NPs. Given that the two-and three-body interactions can be easily disentangled in our ML potential, this allowed us to dissect the role of three-body interactions in the formation of each phase.