A force-based gradient descent method for $\mathit{\text{ab initio}}$ atomic structure relaxation

TL;DR

WANBB is a new force-based gradient descent algorithm for ab initio atomic structure relaxation that significantly reduces computational cost, speeds up convergence, and is robust across diverse systems without requiring prior physical knowledge.

Contribution

The paper introduces WANBB, a novel line minimization approach that improves efficiency and robustness in ab initio atomic structure relaxation compared to traditional methods.

Findings

WANBB reduces the cost of unaccepted trial steps significantly.

WANBB demonstrates universal speedups over conjugate gradient methods.

WANBB is robust and simple to implement without parameter tuning.

Abstract

Force-based algorithms for $\mathit{\text{ab initio}}$ atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive $\mathit{\text{ab initio}}$ calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning.