Parametrization of interatomic potential functions using a genetic algorithm accelerated with a neural network

A genetic algorithm (GA) can be used to fit highly nonlinear functional forms, such as empirical interatomic potentials from a large ensemble of data. The performance of a GA for fitting such functional forms is enhanced through an approach that is based on the use of a neural network (NN) to accelerate the computation of the fitness function for the GA. Application of the new approach for fitting an ensemble of potentials computed from ab initio calculations to a specified functional form (here, the Tersoff potential functional form is used as an example) has shown that the computational efficiency achieved through the use of a NN can reduce computational time by over two orders of magnitude. The potentials estimated from functions thus fitted were within 0.1% of the actual potential values. Specifically, the mean squared error (MSE) on molecular potentials was < 10(-5) eV(2) for fitting Tersoff potentials, and < 0.0025 eV(2) for fitting ab initio potential energies of isolated, 5-atom silicon clusters. Furthermore, since the potential was fitted to a physically meaningful Tersoff functional form, the resulting potential function appears to have the ability to extrapolate over a reasonable range of the parameter space, and may have a better accuracy in estimating the forces compared to that obtained from neural networks, which are often highly inaccurate when extrapolated. Hence, the method can be useful for rendering various molecular dynamics (MD) simulations more tractable. It is also apparent, based on the present investigation, that a Tersoff potential, albeit with different (GA parametrized) coefficients, is adequate for representing the ab initio potentials of 5-atom Si clusters.