Committor-regularized learning of differentiable collective variables from non-differentiable structural descriptors.

Area of Science:

• Computational physics
• Materials science
• Chemical physics

Background:

• Collective variables (CVs) are crucial for molecular simulations, but their construction is limited to differentiable functions of atomic coordinates.
• Discrete structural descriptors, useful for analysis, cannot be directly used for enhanced sampling due to non-differentiability.

Purpose of the Study:

• To develop a physics-informed machine-learning framework to create differentiable CVs from non-differentiable descriptors.
• To enable the use of powerful discrete structural classifiers in enhanced-sampling molecular dynamics simulations.
• To improve the interpretability and reproducibility of machine-learned CVs.

Main Methods:

• Utilized graph neural networks to learn smooth, differentiable surrogate representations of discontinuous descriptors.
• Introduced committor regularization, derived from transition path theory, to guide learning toward committor-like behavior.
• Applied the framework to crystal nucleation in copper melt using polyhedral template matching (PTM) as the target descriptor.

Main Results:

• Successfully trained neural network CVs to reproduce PTM-inferred local crystal structure fractions (FCC, BCC) while remaining differentiable.
• Demonstrated that committor-regularized models produce reproducible free-energy surfaces, overcoming common stochastic variability.
• Showcased the framework's ability to bridge discrete, physics-based descriptors with continuous, differentiable representations.

Conclusions:

• Established a general method for constructing interpretable, reproducible, and physically grounded CVs for enhanced sampling.
• Overcame limitations of non-differentiable descriptors in molecular dynamics simulations.
• Enabled the direct application of discrete structural analysis tools to bias molecular simulations.