Calculating Pairwise Similarity of Polymer Ensembles via Earth Mover's Distance

Synthetic polymers, in contrast to small molecules and deterministic biomacromolecules, are typically ensembles composed of polymer chains with varying numbers, lengths, sequences, chemistry, and topologies. While numerous approaches exist for measuring pairwise similarity among small molecules and sequence-defined biomacromolecules, accurately determining the pairwise similarity between two polymer ensembles remains challenging. This work proposes the earth mover's distance (EMD) metric to calculate the pairwise similarity score between two polymer ensembles. EMD offers a greater resolution of chemical differences between polymer ensembles than the averaging method and provides a quantitative numeric value representing the pairwise similarity between polymer ensembles in alignment with chemical intuition. The EMD approach for assessing polymer similarity enhances the development of accurate chemical search algorithms within polymer databases and can improve machine learning techniques for polymer design, optimization, and property prediction.