Molecular dynamics (MD) simulations are used in diverse
scientific
and engineering fields such as drug discovery, materials design, separations,
biological systems, and reaction engineering. These simulations generate
highly complex data sets that capture the 3D spatial positions, dynamics,
and interactions of thousands of molecules. Analyzing MD data sets
is key for understanding and predicting emergent phenomena and in
identifying key drivers and tuning design knobs of such phenomena.
In this work, we show that the Euler characteristic (EC) provides
an effective topological descriptor that facilitates MD analysis.
The EC is a versatile, low-dimensional, and easy-to-interpret descriptor
that can be used to reduce, analyze, and quantify complex data objects
that are represented as graphs/networks, manifolds/functions, and
point clouds. Specifically, we show that the EC is an informative
descriptor that can be used for machine learning and data analysis
tasks such as classification, visualization, and regression. We demonstrate
the benefits of the proposed approach through case studies that aim
to understand and predict the hydrophobicity of self-assembled monolayers
and the reactivity of complex solvent environments.