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The typically rugged nature of molecular free energy landscapes can frustrateefficient sampling of the thermodynamically relevant phase space due to thepresence of high free energy barriers. Enhanced sampling techniques can improvephase space exploration by accelerating sampling along particular collectivevariables (CVs). A number of techniques exist for data-driven discovery of CVsparameterizing the important large scale motions of the system. A challenge toCV discovery is learning CVs invariant to symmetries of the molecular system,frequently rigid translation, rigid rotation, and permutational relabeling ofidentical particles. Of these, permutational invariance have proved apersistent challenge in frustrating the the data-driven discovery ofmulti-molecular CVs in systems of self-assembling particles andsolvent-inclusive CVs for solvated systems. In this work, we integratePermutation Invariant Vector (PIV) featurizations with autoencoding neuralnetworks to learn nonlinear CVs invariant to translation, rotation, andpermutation, and perform interleaved rounds of CV discovery and enhancedsampling to iteratively expand sampling of configurational phase space andobtain converged CVs and free energy landscapes. We demonstrate thePermutationally Invariant Network for Enhanced Sampling (PINES) approach inapplications to the self-assembly of a 13-atom Argon cluster,association/dissociation of a NaCl ion pair in water, and hydrophobic collapseof a C45H92 n-pentatetracontane polymer chain. We make the approach freelyavailable as a new module within the PLUMED2 enhanced sampling libraries.

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