Based on the eigenvector continuation, which is mathematically an instance of the reduced basis method (RBM), we construct an emulator for coupled-channels calculations for heavy-ion fusion reactions at energies around the Coulomb barrier. We apply this to the ${}^{16}\mathrm{O}+{}^{144,154}\mathrm{Sm},{}^{186}\mathrm{W}$ reactions and examine whether the emulator can be used to extract the deformation parameters of the target nuclei. We show that the emulator not only accelerates the calculations but also has an ability to accurately extract the nuclear shapes. This indicates that the emulator provides a powerful tool to systematically explore intrinsic shapes of atomic nuclei, enhancing our understanding of the fundamental properties of nuclear systems.

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• Nuclear fusion
• Nuclear reactions
• Optical, coupled-channel & distorted wave models