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We study the Landau-Ginzburg mirror of toric/non-toric blowups of (possiblynon-Fano) toric surfaces arising from SYZ mirror symmetry. Through theframework of tropical geometry, we provide an effective method for identifyingthe precise locations of critical points of the superpotential, and furthershow their non-degeneracy for generic parameters. Moreover, we prove that thenumber of geometric critical points equals the rank of cohomology of thesurface, which leads to its closed-string mirror symmetry due to Bayer'searlier result.

Morse superpotentials and blow-ups of surfaces