Genetic programming for multitimescale modeling

A bottleneck for multitimescale thermally activated dynamics is the computation of the potential energy surface. We explore the use of genetic programming GP to symbolically regress a mapping of the saddlepoint barriers from only a few calculated points via molecular dynamics, thereby avoiding explicit calculation of all barriers. The GP-regressed barrier function enables use of kinetic Monte Carlo to simulate real-time kinetics seconds to hours based upon realistic atomic interactions. To illustrate the concept, we apply a GP regression to vacancy-assisted migration on a surface of a concentrated binary alloy from both quantum and empirical potentials and predict the diffusion barriers within 0.1% error from 3% or less of the barriers. We discuss the significant reduction in CPU time 4 to 7 orders of magnitude, the efficacy of GP over standard regression, e.g., polynomial, and the independence of the method on the type of potential.