(462c) Local-Environment-Based Distance Metric for Dimensionality Reduction in Colloidal Self-Assembly

Formulating low-dimensional descriptions of complex, dynamical systems is an area of major scientific and technological interest.  These low-dimensional descriptions are used to develop computationally tractable models of complex systems and, thus, enable engineering analyses and precise control strategies over these systems. Diffusion mapping is a machine learning technique that can provide dynamically rigorous low-dimensional descriptions for complex systems. This technique has been applied successfully to describe a broad range of physical phenomena from protein folding to colloidal nucleation.

In order to apply diffusion mapping to a particular physical problem the use of a specified distance metric is required.  This distance metric should be able to accurately capture the differences between different physical states of the complex physical system under consideration. In this presentation, we will focus on dynamical systems consisting of discrete particles and compare the diffusion mapping results according to three such different distance metrics, namely, the Hausdorff distance, the earth mover’s distance, and a novel distance metric based on a description of the average local environment surrounding each individual particle.  Each of these three distance metrics is applied to describe the directed self-assembly of a quasi-two-dimensional collection of O(100) colloidal particles. This colloidal system exhibits complex behavior, including order-to-disorder transitions, as well as formation of various micro-structural defects in crystalline assemblies of colloidal particles. This variety in the system structure and physical behavior requires a distance metric which is able to consistently distinguish between different configurations characterized by a broad range of different structural features.  This is captured successfully by our local-environment-based description for this system, which is superior to the other distance metrics examined in describing structural diversity.