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Searching for globally optimal functional forms for interatomic potentials using genetic programming with parallel tempering

Journal of Computational Chemistry

Slepoy, Alexander S.; Peters, Michael D.; Thompson, Aidan P.

Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms. © 2007 Wiley Periodicals, Inc.

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Graduated embodiment for sophisticated agent evolution and optimization

Boslough, Mark B.; Peters, Michael D.; Pierson, Arthurine R.

We summarize the results of a project to develop evolutionary computing methods for the design of behaviors of embodied agents in the form of autonomous vehicles. We conceived and implemented a strategy called graduated embodiment. This method allows high-level behavior algorithms to be developed using genetic programming methods in a low-fidelity, disembodied modeling environment for migration to high-fidelity, complex embodied applications. This project applies our methods to the problem domain of robot navigation using adaptive waypoints, which allow navigation behaviors to be ported among autonomous mobile robots with different degrees of embodiment, using incremental adaptation and staged optimization. Our approach to biomimetic behavior engineering is a hybrid of human design and artificial evolution, with the application of evolutionary computing in stages to preserve building blocks and limit search space. The methods and tools developed for this project are directly applicable to other agent-based modeling needs, including climate-related conflict analysis, multiplayer training methods, and market-based hypothesis evaluation.

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