Implicit Differentiation of Energy Landscapes for One-Shot UQ and Fine-Tuning

Interatomic potentials are essential to escape ab initio size limitations, but energies and structures depend sensitively on potential parameters. Gauging the effect of parameter variation typically requires expensive resampling, complicating uncertainty quantification and emerging inverse design schemes which use parameters as a proxy for composition. Here, we Taylor expand the structure and energy of relaxed minima through implicit differentiation, using automatic differentiation, dense linear algebra or a novel sparse operator approach. The memory requirement of automatic differentiation is prohibitive for more than a thousand atoms, but our sparse approach is a linear scaling solution applicable to large systems. Our expansion is able to predict large changes in the formation energy and volume of point defects using classical and machine-learning potentials. We also use the implicit derivative for potential fine-tuning in a targeted structure search, finding solute interactions which induce dislocation core reconstruction and thus solid solution strengthening in bcc tungsten.