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We develop a method that uses truncation-order-dependent re-expansionsconstrained by generic strong-coupling information to extrapolate perturbationseries to the nonperturbative regime. The method is first benchmarked against azero-dimensional model field theory and then applied to the dilute Fermi gas inone and three dimensions. Overall, our method significantly outperforms Pad\'eand Borel extrapolations in these examples. The results for the ground-stateenergy of the three-dimensional Fermi gas are robust with respect to changes ofthe form of the re-expansion and compare well with quantum Monte Carlosimulations throughout the BCS regime and beyond.

From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems