A random walk in function space: Statistical optimization of functional forms for physical models

For computer simulations of physical systems, it is necessary to obtain models that represent the underlying physics, while reducing the computational complexity required for its evaluation. Traditionally, this model construction has been a very time-consuming task. We present a method that allows us to automatically derive symbolic forms of model Hamiltonians from reference data that can be obtained from higher accuracy calculations, such as electronic structure methods and from experimental input. Our method is based on Gene Expression Programming (GEP) [1] techniques to sample the space of possible functional forms of classical Hamiltonians by statistical sampling of symbolic representations that guarantee well-formed expressions within a genetic algorithm. We compare the original GEP method to our two-step approach that separates functional and parameter optimization for test cases of function fitting and reproduction of pair-potentials and we show the performance improvements due to this decomposition of search spaces.

[1] C. Ferreira, Complex Systems 13, 87 (2001).