Energy landscapes for machine learning.

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions.

Structural analysis of high-dimensional basins of attraction.

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties.

Energy landscapes for a machine learning application to series data.

Methods developed to explore and characterise potential energy landscapes are applied to the corresponding landscapes obtained from optimisation of a cost function in machine learning. We consider neural network predictions for the outcome of local geometry optimisation in a triatomic cluster, where four distinct local minima exist. The accuracy of the predictions is compared for fits using data from single and multiple points in the series of atomic configurations resulting from local geometry optimisation and for alternative neural networks.

Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings.

We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys.

Communication: Analysing kinetic transition networks for rare events.

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely.

Visualizing basins of attraction for different minimization algorithms.

We report a study of the basins of attraction for potential energy minima defined by different minimization algorithms for an atomic system. We find that whereas some minimization algorithms produce compact basins, others produce basins with complex boundaries or basins consisting of disconnected parts. Such basins deviate from the "correct" basin of attraction defined by steepest-descent pathways, and the differences can be controlled to some extent by adjustment of the maximum step size.

The ultimate fate of supercooled liquids.

In recent years it has become widely accepted that a dynamical length scale ξ(α) plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing ξ(α) and the size of the crystal nucleus, ξ(M), which shrinks on cooling. We argue that at low temperatures where ξ(α) > ξ(M) a new crystallization mechanism emerges, enabling rapid development of a large scale web of sparsely connected crystallinity.

On the surface of glasses.

Dynamics near the surface of glasses is generally much faster than in the bulk. Neglecting static perturbations of structure at the surface, we use random first order transition (RFOT) theory to show the free energy barrier for activated motion near a free surface should be half that of the bulk at the same temperature. The increased mobility allows the surface layers to descend much further on the energy landscape than the bulk ordinarily does.

Constructing explicit magnetic analogies for the dynamics of glass forming liquids.

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

Thermodynamic-kinetic correlations in supercooled liquids: a critical survey of experimental data and predictions of the random first-order transition theory of glasses.

Thermodynamics and kinetics are thought to be linked in glass transitions. The quantitative predictions of alpha-relaxation activation barriers provided by the theory of glasses based on random first-order transitions are compared with the experimental results for 44 substances. The agreement found between the predicted activation energies near T(g) and experiment is excellent.