GraphVAMPnets for Uncovering Slow Collective Variables of Self-Assembly Dynamics

Abstract

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack the high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenge. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, like tICA, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets which combines graph neural networks with variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in a high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory that studies Markov processes without forcing detailed balance constraint, which addresses the out-of-equilibrium challenge in self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: aggregation of two hydrophobic molecules and self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely to applied to molecular self-assembly.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

“…At the level of the network architecture, Winter, Noé, and Clevert developed a permutation-invariant graph autoencoder (PIGAE) for graph reconstruction by employing an explicit permuter that learns an explicit permutation matrix for each input graph, although the quartic scaling in reordering operations during each training step makes this approach expensive . Similarly, Huang and co-workers developed a GraphVAMPnets-based approach that utilizes graph neural networks to respect permutation and rotational symmetries of particles in self-assembling systems by enforcing identical node embeddings for such symmetric particles and learn the slow CVs from the resulting graph embeddings using VAMPnets. Prudente, Acioli, and Soares Neto and Nguyen and Le developed special purpose neural networks for the fitting of potential energy surfaces of small molecules in which the first layer of the network was modified to respect permutational invariance, although generalization and scaling to larger systems are challenging.…”