(169ao) Permutationally Invariant Network for Enhanced Sampling (PINES): A General Approach to Treating Identical Particles and Constructing Targeted CVs with Machine Learning

Collective variable (CV) based enhanced sampling techniques are commonly used to address the presence of high free energy barriers in molecular simulation and to subsequently improve sampling of phase space. Data-driven methods present a powerful means to identify high-quality CVs¹. It is often desirable to learn CVs respecting the underlying symmetries of the molecular system such as translational, rotational, and permutational invariances. Determination of CVs invariant or equivariant to translation and/or rotation can be readily achieved by data preprocessing or the use of specialized learning architectures², but it has proven more challenging to engage the permutational invariance associated with the atomic or molecular indistinguishability³. We introduce Permutationally Invariant Networks for Enhanced Sampling (PINES)⁴ as a data driven method for learning translationally, rotationally, and permutationally adapted CVs and demonstrate its application to a series of test systems, including Lenard-Jones clusters, ion association in water, and hydrophobic polymer collapse. Here we present recent innovations in our code to generalize PINES to arbitrary systems and detail a systematic user guide to application through the enhanced sampling software suites PLUMED2⁵ and SSAGES⁶.

References:

(1) Sidky, H.; Chen, W.; Ferguson, A. L. Machine Learning for Collective Variable Discovery and Enhanced Sampling in Biomolecular Simulation. Molecular Physics 2020, 118 (5), e1737742. https://doi.org/10.1080/00268976.2020.1737742.

(2) Atz, K.; Grisoni, F.; Schneider, G. Geometric Deep Learning on Molecular Representations. arXiv December 31, 2021. http://arxiv.org/abs/2107.12375.

(3) Noé, F.; Tkatchenko, A.; Müller, K.-R.; Clementi, C. Machine Learning for Molecular Simulation. Annual Review of Physical Chemistry 2020, 71 (1), 361–390. https://doi.org/10.1146/annurev-physchem-042018-052331.

(4) Herringer, N. S. M.; Dasetty, S.; Gandhi, D.; Lee, J.; Ferguson, A. L. Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multi-Molecular and Solvent-Inclusive Collective Variables. arXiv August 16, 2023. https://doi.org/10.48550/arXiv.2308.08680.

(5) Tribello, G. A.; Bonomi, M.; Branduardi, D.; Camilloni, C.; Bussi, G. PLUMED 2: New Feathers for an Old Bird. Computer Physics Communications 2014, 185 (2), 604–613. https://doi.org/10.1016/j.cpc.2013.09.018.

(6) Sidky, H.; Colón, Y. J.; Helfferich, J.; Sikora, B. J.; Bezik, C.; Chu, W.; Giberti, F.; Guo, A. Z.; Jiang, X.; Lequieu, J.; Li, J.; Moller, J.; Quevillon, M. J.; Rahimi, M.; Ramezani-Dakhel, H.; Rathee, V. S.; Reid, D. R.; Sevgen, E.; Thapar, V.; Webb, M. A.; Whitmer, J. K.; de Pablo, J. J. SSAGES: Software Suite for Advanced General Ensemble Simulations. The Journal of Chemical Physics 2018, 148 (4), 044104. https://doi.org/10.1063/1.5008853.