Duane D. Johnson
University of Illinois at Urbana-Champaign, USA

Genetic Programming for Multi-Timescale Modeling and a Separate Approach for Coupling O(N) Atomistic Methods with DG-FEM Calculations

A bottleneck for multi-timescale modeling is the computation of potential energy surface, PES. We explore the use of genetic programming (GP) - a genetic algorithm that evolves computer programs - to perform symbolic regression to create a local mapping of the activation energy for any possible configuration, thereby avoiding explicit calculation of the entire PES. To exemplify the ideas as proof-in-principle, we apply a simple GP to vacancy-assisted migration on a surface of an fcc A(x)B(1-x) alloy which exhibits phase separation. The GP predicts activation energies within 1% error using explicit calculations for less than 3% of the total active configuration. These initial results scale kinetic (Monte Carlo) simulations by~9 orders in time at 300 K over molecular dynamics, and with substantially less CPU time.

In addition, we share our initial ideas for quasi-static calculations that coupling O(N) atomistic calculations within a framework of discontinuous Galerkin FEM. We are developing the approach to be object-oriented and therefore independent of underlying atomistic approach (e.g., pair-potentials, tight-binding, full band-structure) but share and evolve information with the continuum in a controlled manner.