Active-subspace learning reveals dominant parameter directions in nuclear observables

Nuclear observables computed using ab initio methods can depend on many low-energy constants (LECs) of the underlying chiral effective field theory interactions, while being sensitive to only a few LEC combinations. We use active-subspace learning to identify these dominant parameter directions directly from many-body calculations. For ground-state energies and charge radii of oxygen isotopes, we find that more than 99% of the gradient-based variation is concentrated along a single direction for each observable in the 17-dimensional LEC space. Comparing these directions across nuclei and observables quantifies similarities in their LEC dependence. The same analysis yields derivative-based global sensitivities without requiring a global emulator. Active-subspace directions can also serve as an efficient representation for emulation, greatly improving Gaussian-process emulators especially for broad LEC variations. We demonstrate this for Hartree-Fock calculations of $^{48}\mathrm{Ca}$, where the emulator error is improved with active-subspace learning by more than two orders of magnitude.