Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations

Area of Science:

• Computational Chemistry and Physics
• Statistical Mechanics
• Data Science

Background:

• Enhanced sampling methods are crucial for simulating complex dynamical systems in chemistry and physics.
• Identifying appropriate collective variables (CVs) to guide these simulations is challenging and often relies on chemical intuition.
• Existing manifold learning techniques struggle to provide accurate CVs from enhanced sampling data due to biased sampling.

Purpose of the Study:

• To develop a general reweighting framework for manifold learning that corrects for biased probability distributions in enhanced sampling simulations.
• To enable the accurate construction of low-dimensional collective variables (CVs) directly from enhanced sampling simulation data.
• To provide a method that overcomes the limitations of current manifold learning approaches in the context of biased sampling.

Main Methods:

• Developed a reweighting framework based on anisotropic diffusion maps for manifold learning.
• Accounted for biased probability distributions in the learning dataset.
• Constructed a Markov chain to model transition probabilities between high-dimensional samples.

Main Results:

• The proposed framework successfully reverts the biasing effect of enhanced sampling simulations.
• Yielded collective variables (CVs) that accurately describe the equilibrium probability density.
• Demonstrated the applicability of the reweighted manifold learning framework to various manifold learning techniques and simulation data.

Conclusions:

• Reweighted manifold learning enables accurate construction of low-dimensional CVs from enhanced sampling simulations.
• This advancement overcomes a critical limitation in applying manifold learning to biased simulation data.
• The framework offers a general solution applicable to both standard and enhanced sampling simulations for improved analysis.