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Bayesian inverse statistical mechanics

Many interesting and industrially important phenomena in condensed matter physics and materials science are described by equilibrium statistical mechanics. Predicting these phenomena from the atomic potential energy function is an example of the forward problem in statistical mechanics. Such calculations require the accurate determination of the atomistic potential energy function at points throughout the high probability region of configuration space: a space with total volume that scales exponentially in the number of atoms used for the simulation. Accurate statistical mechanical calculations for fluids and disordered systems typically require tens of millions of single point evaluations. At the same time, accurate single point calculations based on quantum mechanics typically take hours of CPU time. There is therefore a need for faster sampling algorithms and faster methods for calculating the potential energy function without sacrificing accuracy. In this project, the student will calculate a probability distribution over a space of inter-atomic potential energy functions. This will be performed by employing Nested Sampling to perform Bayesian model selection and parameter estimation, using empirical and simulated data for the radial distribution function measured at a series of temperatures. Inferring the potential energy function from experimental data is an example of an inverse problem in statistical mechanics. The resulting potential energy function will require thousands of seconds to calculate on a single CPU with one hundred atoms, and will reproduce the radial distribution function. Many important thermodynamic quantities, including the general PVT equation of state are directly related to the radial distribution function. This strongly suggests that the inferred potentials will also reproduce those quantities. In the second phase of the project the student will test the predictive power of the inferred potential energy functions by applying Nested Sampling to calculate the complete phase diagram and comparing this to the experimentally determined phase diagram.