Understanding locality of interaction, or other forms of sparsity, in *ab initio* models can be effectively exploited to construct highly efficient and accurate multi-scale schemes e.g. of QM/MM type. In QM/MM schemes we model regions of interest, such as a dislocation core in the following figure, using an electronic structure model, while the material bulk is modelled with a computationally inexpensive interatomic potential model.

Upon increasing the QM core region, the accuracy of the simulation should, in principle, increase, such as the following figure:

However, various artefacts in commonly used QM/MM schemes prevent this. The main new idea that made this figure possible is that we construct interatomic potentials (or forces) that are *tuned to interact well with the QM model* rather than using "off-the-shelf potentials". This yields new QM/MM schemes with rigorous convergence rates in terms of the QM region size. [56], [57], [58]