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

Abstract

The typically rugged nature of molecular freeenergy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Data-Driven Path Collective Variables

“…In this way, each component in ξ has a corresponding weight which encodes its importance: a low σ means that the corresponding CV component is highly correlated to the committor. ξ can be composed of simple, intuitive CVs but can also include high-dimensional, abstract representations such as commonly used local descriptors for machine-learned interatomic potentials (e.g., atom-centered symmetry functions and the smooth overlap of atomic positions (SOAP)) or global variants such as the permutation-invariant vector (PIV). ,, Optimal values for σ and the regularization parameter λ are obtained through optimization by minimizing a loss function based on a training set, distinct from the set of configurations used in KRR (the reference set).…”

Enhanced Sampling of Crystal Nucleation with Graph Representation Learnt Variables

“…Different from the above two hand-crafted classes of OPs, recent breakthroughs in machine learning (ML) techniques have given rise to a range of neural network (NN)-based OPs for a variety of problems, including crystal nucleation. The inherent differentiability of these OPs makes them suited for various enhanced sampling methods that involve the modification of a system’s Hamiltonian. − We specifically highlight graph neural networks (GNNs), which have emerged as powerful tools in the realm of materials science, including but not limited to efficient descriptions of material energetics, , accurate predictions on material properties, , and robust classifiers of crystal structures and defects. − …”