Constructing convex energy landscapes for atomistic structure optimization

Abstract

We propose a global optimization strategy for atomistic structure determination based on two new concepts: a few-atom complementary energy landscape and atomic role models. Global optimization of costly energy expressions may be aided by performing some of the optimization on model energy landscapes. These are often based on a sum-of-atomic-contributions form that accurately reproduces every local energy minimum of the true energy expression. However, we propose that, by not including all atomic contributions, the resulting energy landscapes may become more convex, making the search for the global optimum more facile. A role model is someone we aspire to be more like; in the same vein we define the role model of an atom to be another atom whose local environment the first atom seeks to obtain itself. Basing a complementary energy landscape on the distance of some atoms from their role models in a feature space, we arrive at a useful few-atom complementary energy landscape. We show that relaxation in this landscape is an effective mutation when employed in an evolutionary algorithm used to identify the bulk cristobalite structure of SiO 2 and the (1 × 4) surface reconstruction of anatase TiO 2 (001).

Structure prediction of surface reconstructions by deep reinforcement learning

“…Effectively, two xz-grids are introduced, each with two channels (one for each atom type), coinciding with the bulk positions of TiO 2 under periodic be performed. To on the computational demand, we employ density functional based tight binding (DFTB) calculations that are faster than full DFT For DFTB we use parameters from reference [62], which known to reproduce the correct global minimum [46]. ASLA hyperparameters are given in section computational information.…”

“…To deal with the complexity problem efficiently, efforts have been put into changing the inherently stochastic nature of the aforementioned structure prediction algorithms, to algorithms that make informed choices [42][43][44][45][46]. Such methods are capable of traversing the configurational and compositional spaces more efficiently, thereby opening up for tackling more complex problems.…”

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

“…[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Machine learning has also led to substantial improvements for optimization algorithms, such as algorithms being enhanced by the usage of machine learning potentials [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] or by utilizing machine learning to more efficiently generate candidate structures that progress the search. [51][52][53][54][55][56][57][58][59][60][61][62] With the speed of advancement in the materials science and machine learning communities it is essential that software tools are available that allow quick experimentation. This is especially true for global optimization (GO), an open-ended subject with room for new and improved algorithms.…”

Gaussian representation for image recognition and reinforcement learning of atomistic structure

“…Rather, the ML models may provide local energy information, 35,36 serve to provide uncertainty measures to balance exploration vs exploitation, [37][38][39] or act to remove energy barriers by adding extra dimensions 40 or making energy landscapes simpler and more convex. 41,42 Recently, an entirely different approach to global structure optimization, namely, utilizing reinforcement learning, was proposed. 43,44 In our work, 43 we utilize image recognition techniques to have a machine learning agent learn by itself how to build atomistic structures.…”