Fig. 1
From: Towards exact molecular dynamics simulations with machine-learned force fields
Fully data-driven symmetry discovery. a, b Our multipartite matching algorithm recovers a globally consistent atom-atom assignment across the whole training set of molecular conformations, which directly enables the identification and reconstructive exploitation of relevant spatial and temporal physical symmetries of the molecular dynamics. c The global solution is obtained via synchronization of approximate pairwise matchings based on the assignment of adjacency matrix eigenvectors, which correspond in near isomorphic molecular graphs. We take advantage of the fact that the minimal spanning set of best bipartite assignments fully describes the multipartite matching, which is recovered via its transitive closure. Symmetries that are not relevant within the scope of the training dataset are successfully ignored. d This enables the efficient construction of individual kernel functions for each training molecule, reflecting the joined similarity of all its symmetric variants with another molecule. The kernel exercises the symmetries by consolidating all training examples in an arbitrary reference configuration from which they are distributed across all symmetric subdomains. This approach effectively trains the fully symmetrized dataset without incurring the additional computational cost
