Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations

Abstract

Enhanced sampling methods are indispensable in computational physics and chemistry, where atomistic simulations cannot exhaustively sample the high-dimensional configuration space of dynamical systems due to the sampling problem. A class of such enhanced sampling methods works by identifying a few slow degrees of freedom, termed collective variables (CVs), and enhancing the sampling along these CVs. Selecting CVs to analyze and drive the sampling is not trivial and often relies on physical and chemical intuition. Despite routinely circumventing this issue using manifold learning to estimate CVs directly from standard simulations, such methods cannot provide mappings to a low-dimensional manifold from enhanced sampling simulations as the geometry and density of the learned manifold are biased. Here, we address this crucial issue and provide a general reweighting framework based on anisotropic diffusion maps for manifold learning that takes into account that the learning data set is sampled from a biased probability distribution. We consider manifold learning methods based on constructing a Markov chain describing transition probabilities between high-dimensional samples. We show that our framework reverts the biasing effect yielding CVs that correctly describe the equilibrium density. This advancement enables the construction of low-dimensional CVs using manifold learning directly from data generated by enhanced sampling simulations. We call our framework reweighted manifold learning. We show that it can be used in many manifold learning techniques on data from both standard and enhanced sampling simulations.

Published version

References in corpus (23)

• Canonical sampling through velocity-rescaling
• Escaping free-energy minima
• PLUMED 2: New feathers for an old bird
• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• Theoretical perspective on the glass transition and amorphous materials
• Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations
• Accurate sampling using Langevin dynamics
• Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration
• Equilibrium free energies from non-equilibrium metadynamics
• Enhanced sampling methods for molecular dynamics simulations
• A Variational Approach to Enhanced Sampling and Free Energy Calculations
• Caliber based spectral gap optimization of order parameters (SGOOP) for sampling complex molecular systems
• iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes
• Accelerated weight histogram method for exploring free energy landscapes
• Frequency adaptive metadynamics for the calculation of rare-event kinetics
• Unfolding Hidden Barriers by Active Enhanced Sampling
• Multiscale reweighted stochastic embedding (MRSE): Deep learning of collective variables for enhanced sampling
• Finding Multiple Reaction Pathways of Ligand Unbinding
• Dynamical reweighting methods for Markov models
• Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems
• Estimation of the infinitesimal generator by square-root approximation
• Conformational Entropy as Collective Variable for Proteins
• Visualising energy landscapes through manifold learning

Cited by in corpus (7)

• Reaction Coordinates for Conformational Transitions using Linear Discriminant Analysis on Positions
• Spectral Map: Embedding Slow Kinetics in Collective Variables
• Manifold Learning in Atomistic Simulations: A Conceptual Review
• Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps
• Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles
• Learning Markovian Dynamics with Spectral Maps
• Fast Sampling of Protein Conformational Dynamics