  We interpret the Landau-Ginzburg potentials associated to
Gross-Hacking-Keel-Kontsevich's partial compactifications of cluster varieties
as F-polynomials of projective representations of Jacobian algebras. Along the
way, we show that both the projective and the injective representations of
Jacobi-finite quivers with potential are well-behaved under
Derksen-Weyman-Zelevinsky's mutations of representations.
