Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds

We prove that smooth Fano threefolds have toric Landau–Ginzburg models. More precise, we prove that their Landau–Ginzburg models, presented as Laurent polynomials, admit compactifications to families of K3 surfaces, and we describe their fibers over infinity. We also give an explicit construction of Landau–Ginzburg models for del Pezzo surfaces and any divisors on them.