Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic

18 July 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


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 datasets that capture the 3D spatial positions, dynamics, and interactions of thousands of molecules. Analyzing MD datasets 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.


Molecular Simulation
Data Science

Supplementary materials

Supporting Information: Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic
Describes computational methods for the studied molecular simulation datasets and for the computation of the Euler characteristic of both graph and manifold data representations.


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