Genetic Programming for Multiscale Modeling

We propose the use of genetic programming (GP)—a genetic algorithm that evolves computer programs—for bridging simulation methods across multiple scales of time and/or length. The effectiveness of genetic programming in multiscale simulation is demonstrated using two illustrative, non-trivial case studies in science and engineering. The first case is multi-timescale materials kinetics modeling, where genetic programming is used to symbolically regress a mapping of all diffusion barriers from only a few calculated ones, thereby avoiding explicit calculation of all the barriers. The GP-regressed barrier function enables use of kinetic Monte Carlo for realistic potentials and simulation of realistic experimental times (seconds). Specifically, a GP regression is applied to vacancy-assisted migration on a surface of a binary alloy and predict the diffusion barriers within 0.1–1% error using 3% (or less) of the barriers. The second case is the development of constitutive relation between macroscopic variables using measured data, where GP is used to evolve both the function form of the constitutive equation as well as the coefficient values. Specifically, GP regression is used for developing a constitutive relation between flow stress and temperature-compensated strain rate based on microstructural characterization for an aluminum alloy AA7055. We not only reproduce a constitutive relation proposed in literature, but also develop a new constitutive equation that fits both low-strain-rate and high-strainrate data. We hope these disparate example applications exemplify the power of GP for multiscaling at the price, of course, of not knowing physical details at the intermediate scales.