Presently, there are two ways to calculate the nuclear force, or if you prefer, the "residual" strong force, from Quantum Chromodynamics (QCD), which is the fundamental theory for strong interaction.
1) Using lattice QCD which is based on large-scale simulations performed on supercomputers. A couple of recent papers, e.g. Lattice QCD approach to Nuclear Physics by a Japanese group and
Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry by a US group. These two groups are the main ones simulating the nuclear force using lattice QCD.
2) Using effective field theory, which was reviewed in, for instance, Modern Theory of Nuclear Forces. Based on the framework of effective field theory, there are also simulations of nuclei. An important example is the success of calculating the Hoyle state of the carbon nucleus.