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Abstract: Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below $1\%$. Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to $17\%$. This difference is attributed to the VDF closure and moment projection.